Place a large stock pot over HIGH heat. When hot, add the olive oil.
Sear the short ribs on all sides until dark brown (about 2 minutes per side).
Once brown, remove and place in a braising pan or dutch oven.
Discard the oil, add fresh oil, and then saute all vegetables until brown. Add tomato paste and red wine, scraping up all bits of the pan.
Pour the vegetable mixture over the short ribs. Add rosemary and thyme. Add beef broth until ribs are completely submerged.
Cover with a tight fitting lid or aluminum foil and place in the preheated oven. Braising time is between 3-4 hours.
Once the short ribs are tender, remove from the liquid and set them aside on a plate (cover with foil).
Strain the braising liquid and allow to sit and cool for 30 minutes to allow the fat to rise to the top.
Skim the fat off the top using a ladle and discard.
Place the remaining liquid in a sauce pan, add honey and balsamic vinegar, and reduce by half over MEDIUM-HIGH heat. To thicken, mix flour and cold water to create a slurry, then slowly whisk into sauce until desired consistency is reached.
If necessary, reheat the short ribs in the sauce in the oven until hot. Serve.