Can this have an explanation for transgenderism or the notion of a gendered brain?
This response might be long, sorry, but bear with me. I'm walking a line between precision and brevity 
There are sex differences in human brains at the molecular level (as well as at the macro level or size and structure), plus sex differences in susceptibility to disease, mental illness, addiction, etc., and it's a hot topic in research right now to pin down the epigenetic mechanism of these differences. As ever, these are only mean differences (males as a group differ from females as a group) but some of the effect sizes are quite large.
Epigenetics govern huge parts of brain development. All human (and mammal) brains are heading for a female phenotype until hormonal signals from the fetal testes begin to "masculinise" the brain in the time around birth by switching on various genes (and switching off others) concerned with neural development. For the last couple of months of full-term human pregnancy, and the first couple of months of newborn life, a baby boy's brain is developing differently from a baby girl's at both micro and macro level. A good indicator that these changes are epigenetic (rather than driven purely by genes) is Complete Androgen Insensitivity Syndrome, an intersex disorder where XY males are insensitive to male hormones and so their brains never undergo masculinisation: these babies have XY genotype but an XX brain phenotype due to lack of epigenetic change. Bear in mind that even though we talk about masculinised and feminised brains, it's still just average differences: there is immensely more that is similar than different, and it's a spectrum from highly masculinised to highly feminise. It's also not necessarily masculinisation or feminisation of behaviour, just of structure and not across all the parts of the brain equally: only of specific structures, to varying extents.
From this point onwards, most of the research is in mice and rats rather than humans so its applicability is unclear - similar mechanisms are likely to apply to humans, but probably not in exactly the same way. Experiments have shown that when you disrupt brain masculinisation in newborn male rats by chemically switching off relevant genes, so their brains become feminised, they don't show male sexual behaviours (like mounting females) as adults. If you artificially masculinise brains of newborn female rats by switching genes on (or by giving them male hormones), they show male sexual behaviours as adults. You can also somewhat masculinise the brains of older female rats, after the critical newborn period, by switching on the genes but not by simply giving them male hormones. Overall, it looks like male and female rodent brains are bipotential - they can become either epigenetically masculinised or feminised by hormone exposure in a critical period around birth. Once this period is over, there is some fine-tuning possible (perhaps in the hormonal rush of puberty?) but the work of neural sex differentiation is normally fixed shortly after birth.
But enough about rodents. What about gendered brains in humans? In my view, I think it's theoretically likely - but by no means definite - that some human behaviours are similarly epigenetic, but it's more likely to be the instinctual ones that have analogues in other mammals. For instance, stereotypical female nurturing might be due to two waves of epigenetic factors - hormonal brain feminisation around birth that means genes regarding nurturing are switched on and waiting for a trigger, and/or intensive exposure to an infant that acts as a trigger to produce nurturing behaviour. Since it's all probabilistic, it means that some women are not particularly nurturing because their brains weren't highly feminised as a newborn and so the relevant genes are only partially switched on and/or they haven't spent enough time around infants to trigger the behaviour. Likewise, some men are highly nurturing because their brains weren't highly masculinised as a newborn and so the relevant genes are partially switched on and/or they spent intensive periods with infants and so triggered nurturing behaviour. This is just an example I'm making up! There's no evidence for this kind of thing in humans, but it's an example of what's theoretically possible.
As for transgenderism, there's no evidence there either. Some researchers with clear agendas have written about the epigenetic basis of trans identity like it's accepted fact but it most certainly isn't. Masculinisation or feminisation of brain structure says absolutely nothing about gender identity and it's massive overinterpretation to claim that it does. Rodents don't have gender identities and that's where most of the evidence base comes from... At a stretch, it's possible that brain masculinisation or feminisation could set the stage for certain behavioural preferences that are then reinforced. For example, higher levels of male hormones in young children and masculinised brain structure can predict greater preferences for rough and tumble play - if this behaviour is socially reinforced in boys but suppressed in girls, then suddenly perfectly natural variation in child behaviour becomes dichotomised into boy and girl roles. And being constantly told, implicitly or explicitly, that your behaviour is wrong for your sex can't be good for any child's developing sense of self.
One thing I would say that's strongly indicated from animal research is that cross-sex hormones in adulthood (or anytime after the newborn period) cannot completely feminise a male brain or masculinise a female one. While the hormones themselves will have certain effects, the critical window is long closed for them to bring about epigenetic change. Male brains stay masculinised, female brains stay feminised, unless something much more radical than cross-sex hormones are used to alter gene expression.
It's also the case that the "female brain in a male body" narrative doesn't make much sense in terms of neuroepigenetic research. Once a fetus develops male genitalia, its testes will release hormones to masculinise the brain to a greater or lesser extent. If the male hormones aren't released or don't work, you have an intersex condition, which is an entirely different kettle of fish to what counts as trans now. In the absence of intersex conditions, male brains are masculinised, female brains are feminised. Most of the job is done by the age of 2 months, but it might be completed at puberty. Very speculatively, I do wonder if the potential epigenetic fine-tuning at puberty is what leads to desistance in gender dysphoric children.