Preheat oven to 400°F. Wash and dry the potatoes, then prick them with a fork. Rub with olive oil and season with salt. Place on a baking sheet and bake until tender, about 1 hour.
While potatoes bake, heat a skillet over medium heat. Cook ground beef with onions, carrots, and garlic until beef is browned and vegetables are softened. Season with salt and pepper.
Stir in tomato paste, Worcestershire sauce, thyme, and rosemary. Cook for 1 minute, then add beef broth. Bring to a simmer and cook until slightly thickened, about 10 minutes.
Once potatoes are baked, slice them open and fluff the insides with a fork. Spoon the beef mixture into each potato, top with shredded cheese, and return to the oven. Bake until cheese is melted and bubbly, about 10 minutes.