Heat the olive oil in a large 5-to-6 quart Dutch oven or heavy soup pot over medium-high heat. Add the ground beef and cook for 5-7 minutes, breaking it into crumbles, until browned. Drain excess fat if needed.
Add the diced onion, red, green, and yellow bell peppers. Sauté for 6-8 minutes until the peppers soften slightly. Add the minced garlic, Italian seasoning, smoked paprika, salt, and black pepper. Cook for 1 minute until fragrant.
Pour in the fire-roasted diced tomatoes, tomato sauce, and beef broth. Stir well, scraping up any browned bits from the bottom. Bring to a boil, then reduce heat to low, cover, and simmer for 15-20 minutes.
Gently fold in the cooked rice and simmer uncovered for 3-4 minutes until warmed through. Taste and adjust salt and pepper.
Ladle hot soup into bowls. Top with freshly shredded cheddar cheese and chopped fresh parsley. Serve immediately with warm crusty bread.