Place onion, carrots, celery, and garlic into a bowl, toss with the thyme, basil, and oregano and set aside. Preheat braiser or dutch oven on the stovetop over medium-high heat. (I used my Le Creuset braiser.)
Season the short ribs on all sides with salt and pepper.
Once the pan is hot, coat it in a little bit of olive oil.
Sear the short ribs for 2 minutes per side. Remove them from the pan and set aside.
Add veggies from the bowl to the pan.
Cook the veggies, stirring occasionally, until they’ve started to caramelize.
Deglaze the pan with the red wine.
Return the short ribs to the pan and add the beef stock. The liquid should cover about half of the short ribs. Depending on the size of the pan, you may not need all of the beef stock – you don’t want them to be covered up with too much liquid. Add some water if the short ribs aren’t covered by half.
Move the pan to the oven and cook with the lid on for about 2 hours, until the meat easily comes off of the bone.
Cook for an additional 15-20 minutes uncovered, then remove from the oven and let the short ribs rest while you’re making the bolognese.
Place the veggies and herbs (not the ones from the braising liquid) into a blender or food processor and blend into a rough puree. I did this in my Vitamix.
Add the veggies from the braising liquid and continue to puree. It will likely still be a bit rough, which is OK.