Brown the ribs on all sides, about 45 seconds per side, using tongs to turn them as they brown.
Remove the ribs and set aside.
Lower the heat to medium.
Add the onion and carrots to the Dutch oven, and cook for 2 minutes until the onion begins to turn translucent.
Add 1 cup of beef broth and deglaze the pan. Bring everything to a boil and cook for 2 more minutes, scraping all of the crispy bits from the bottom and sides of the pan.
Add the remaining broth, balsamic vinegar, 1 teaspoon of salt, and several turns on a ground pepper grinder.
Stir everything, taste it, and add more salt if desired.
Add the ribs back to the Dutch oven. They should be almost completely submerged.
Add the thyme and rosemary sprigs to the liquid.
Put on the lid and place into the oven.
Cook at 350 for 2 hours.
Reduce heat to 325 and cook for another 30 minutes.
Remove pan from oven and allow to sit with the lid on for at least 20 minutes.