Preheat the oven to 300 degrees. Season the short ribs with salt and pepper and dredge all sides in the flour. Heat the olive oil in a large Dutch oven over medium high heat.
Sear all sides of the ribs until they are evenly browned, about eight minutes. Transfer the ribs to a platter.
Reduce the heat to medium and add the onion, garlic and carrots and cook until the vegetables have softened, about 7 minutes.
Add the tomato paste and cook for about 2 to 3 minutes then add the red wine. Use a wooden spoon to scrape the caramelized bits on the bottom of the pan and allow the wine to reduce for about 3 to 4 minutes.
Next add in the beef broth and return the short ribs to the pot submerging them in the liquid. Bring to a simmer, then cover and transfer the pot to the oven.
The short ribs will braise in the oven for two to three hours depending on how thick they are to begin with. Once the meat is tender and almost falling off the bone, remove the ribs from the pot and transfer them to a large plate.
Serve the ribs over cheesy grits or mashed potatoes and spoon the gravy on top.