Dice or julienne carrots and chop shallots.
Salt and pepper short ribs on all sides, then dredge in flour.
Cook pancetta over medium heat in Dutch Oven until completely crispy and all fat is rendered. Remove pancetta, set aside, but leave fat in pan.
Add olive oil to pan, and raise heat to high. Sear ribs until nicely browned, about 45 seconds per side. Remove ribs and set aside.Turn heat down to medium.
Add onions, carrots, and shallots to pan; cook for 2minutes. Pour in wine and scrape bottom of pan to release any browned bits.Bring to a boil and cook 2 minutes more.
Add broth, 1 tsp. Kosher salt, and freshly ground black pepper to taste. Add ribs, thyme and rosemary sprigs and cooked pancetta to the liquid. Cover with lid place in oven. Cook a 350°F for 2 hours, then reduce heat to 325°F and cook for an additional 30 to 45 minutes. Ribs should be fork tender and falling off the bone.
Remove from pan, remove pan from oven and allow to sit for at least 20 minutes with the lid on prior to serving. Serve over mashed potatoes.