celery....I do not give a stuff if you don't like it, buy some, put it in there! .....chop it very finely and sweat it with the onions
pancetta, or some sort of smokey pig part...again in with the onions
plenty of S&P...again right at the start and some nice stalky bits of thyme/oregano/marjoram or parsley at a pinch
Most importantly make a decent job of sweating this down...don't singe it, you are looking for soft melty translucent veg, with maybe a hint of gold on some of the onions...long low slow heat
You want the opposite for the meat...hot hot lava hot, sear it, as quickly and as high a heat as you can
add mince to veg, deglaze meat pan with something, water, wine, beef stock, add to pan and a tin or two of tomatoes and a squoosh of puree or pesto
I add about half a cup of milk, clamp on the lid (more often than not I finish it in the slow cooker) and cook for ages....If the oven is on it won't hurt for an hour or so in there, lid off for a bit to get properly reduced and a bit toasty round the edges
refine seasoning, maybe more S&P, definitely nutmeg, maybe more oregano.
A decent Bolognese is not to be hurried.