Preheat oven to 300 degrees. Heat oil in a large Dutch oven over medium-high heat. Add the onion, peppers, carrots, celery, and teaspoon of salt. Cook until the onion is softened and translucent.
Add the tomato paste and garlic and cook 2 minutes. Place the short ribs into the pot and toss in the bay leaves and thyme. Pour the wine and broth over the meat. Cover and put into the oven, cook for 4 hours.
Remove the pot from the oven onto a stovetop burner. Remove the meat and meat to a plate to cool. Skim the fat off the top of the liquid in the pot.
Turn the burner to simmer, remove bay leaves, and allow the liquid to simmer uncovered while you separate the meat from the bones and fat. Add the meat back to the pot and continue to simmer until reduced slightly, about 10 minutes.