Drizzle a little olive oil in a Dutch oven. Add ground beef, 1 1/4 teaspoon salt, and 3/4 black pepper to skillet, browning, and crumbling ground beef (1 pound), over medium heat until there is no longer any pink in the meat. Transfer to a paper towel-lined plate.
If there aren't 2 tablespoons of drippings in the skillet, make up the difference with olive oil. Add the onion (1 cup) and bell peppers (2) and sauté over medium, stirring often, until onions are translucent.
Add garlic (1 tablespoon), Italian seasoning (1 tablespoon), and rosemary (1 teaspoon), then continue to sauté, stirring constantly, until garlic and herbs are fragrant, about 1-2 minutes.
Add Worcestershire sauce (1 tablespoon), fire-roasted diced tomatoes (1 can), ketchup, 1 1/4 cups beef broth, 2 cups mozzarella, ground beef, and rice (1 cup), and stir to combine evenly.
Bring the mixture to a boil over medium-high heat. Immediately reduce heat to low and simmer, covered for 20 minutes. Uncover and stir, checking to see if the rice needs more beef broth to cook to tender, cover and finish cooking until rice is tender, about 10-12 minutes.
Remove pot from heat, stir, and adjust seasoning if needed. Sprinkle cheese over top, recover, and let sit, off heat, until cheese is melted about 10 minutes.