Cook onion and ground beef: Heat oil in a Dutch oven over medium-high. Add onion to pan; sauté until onion starts to soften, 3 to 4 minutes. Crumble in beef; cook until beef is mostly browned, 4 to 5 minutes, stirring frequently to crumble. Stir in Italian seasoning, crushed red pepper, garlic, and bell peppers; saute until peppers just start to soften, 2 to 3 minutes.
Add remaining ingredients: Stir in beef stock, marinara sauce, salt, and tomatoes; bring to a boil over high heat. Stir in rice.
Simmer: Reduce heat to medium-low or level required to maintain a steady simmer; partially cover pan and cook until rice is tender, 20 to 23 minutes.
Serve: Ladle soup evenly into bowls; top with cheese.
