So called 'shallow' conversations can go surprisingly deep if you're genuinely interested in the other person and you're willing to open up and share something of yourself too.
If someone is talking about their relationship or kids, you can ask some open questions, like:
"What's been the best thing about being a parent so far?"
"What do you find the most challenging?"
Then as they open up you can reflect back what you're hearing, eg 'It sounds like being a good dad is really important to you but you feel like you're falling short right now. Is that right? ".
You can ask appreciative inquiry questions like "What do you think you do really well?" or "What do you love most about X?"
Questions like "What's important to you about that?" can deepen a conversation and help uncover someone's underlying values and ethics.
Questions like "What sparked your interest in X hobby?" for example will prompt them to tell a story about themselves which can be really eye opening and you can deepen things by reflecting and summarising what you've heard to check that you've understood. "Ah, so you've always been very creative?" "Where do you that came from?"
"It sounds like you really value space/freedom/good time management" and if you've asked in a genuine way and they feel safe then will keep talking and opening up.
Then be willing to share something of yourself too, your own vulnerabilities, hopes and fears. If you open up in a vulnerable way then the other person may also share something surprisingly deep and meaningful in return, as long as they feel safe to do so. Ie "You know sometimes I get really scared about X", and if they're sensitive then they will say "me too!" or share their own fears. That's why this sort of thing can't be contrived. You have to be genuinely caring and interested.
To me, deep and meaningful conversation is about creating heartfelt connection with another human being, rather than pontificating on abstract concepts. If you want the latter then agree with PPs, join debating society