Preheat an oven to 350°F. Generously season the short ribs with salt and pepper.
Add the olive oil to a Dutch oven over medium-high heat. Sear the ribs until browned on all sides, 8 to 10 minutes per batch. Work in batches if necessary, don't crowd the pan or the ribs will steam instead of sear. After each batch is done, transfer the ribs to a platter.
Add the shallots to the pot and sauté for about 3 minutes. You want them to become soft.
Turn up the heat to the Dutch oven and add the balsamic vinegar and red wine. Bring to a simmer. Scrape any browned bits from the pan bottom. Stir in the brown sugar and stock. Bring to a boil.
Return the ribs to the pot, cover the pot, and transfer to the oven. Cook until the meat is tender, about 2 to 2.5 hours.
To serve, skim some of the fat off the top. Good served with mashed potatoes, risotto, grits, or pasta with sauce spooned on top.