Season your short ribs with salt and pepper.
Heat a tbsp olive oil in a pan. When very hot, add the short ribs in batches and cook until browned well on all sides. Use new oil with each batch.
Chop the vegetables into mirepoix (fancy chef term for a medium dice). Heat a tbsp of olive oil in a LARGE pot over medium/low heat. Add the vegetables and sweat. After five minutes add the smashed garlic. Sweat another five minutes.
Add the wine and stock. Bring to a boil. Lower to a simmer. Skim any impurities from the surface (aka any foam, fat, etc.).
Add the short ribs to the simmering cooking liquid. Cover and simmer for at least 3 hours, the longer the better. You can also do this in a crockpot if you have one. Periodically skim any impurities from the surface.
While your short ribs are cooking, prepare your glazed onions. When your meat has finished braising, carefully remove the meat from the pot (it falls apart VERY easily) and place it in a baking dish. Cover with foil.
Strain about 3 cups of the cooking liquid into a saucepan and reduce until it thickens enough to coat the back of a spoon. Taste it. I sometimes add a tsp of sugar for a little extra sweetness. If it needs salt, add a pinch of that too.
Pour the sauce over the short ribs add the glazed onions. Heat in a 300 degree oven for 10 minutes until hot. Serve hot.