Add the 2 tablespoons olive oil to a large skillet and heat over medium-high. Add the 2 pounds bone-in beef short ribs to the pan and sear on all sides for 1-2 minutes until a nice crust has formed. Remove from the pan and place the short ribs in the greased pot of a 7-quart slow cooker.
Add the 1 ½ cups diced onion, and 1 cup diced carrots, to the pan and cook in the remaining oil for 2-3 minutes until the onions are translucent. Add the 3 tablespoons minced garlic, and cook for an additional minute before transferring to the slow cooker.
Cook the 1 pound Italian sausage, in the skillet until no pink remains. Drain off any fat before adding to the slow cooker.
Add the 1 (28-ounce) can whole San Marzano tomatoes, 1 (28-ounce) can crushed San Marzano tomatoes,1 (6-ounce) can tomato paste, ½ cup dry red wine, 1 ½ tablespoons dried basil, 1 tablespoon dried oregano, 2 teaspoons dried thyme, 1 teaspoon kosher salt, and ½ teaspoon ground black pepper to the slow cooker and stir until everything is well combined. It’s alright if the short ribs fall apart as you mix everything.
Cover and cook on LOW for 7-8 hours or on HIGH for 4-5 hours. Shred the short ribs with two forks and discard the bones before serving.
Serve over al dente pasta with pecorino romano cheese on top.