Heat olive oil in a large pot or Dutch oven over medium-high heat. Add the ground beef and cook, breaking it apart with a wooden spoon, until fully browned, about 5 to 6 minutes. Drain any excess grease.
Add the diced onion to the pot and cook until softened, about 3 minutes. Stir in the minced garlic and cook for 30 seconds until fragrant.
Add the diced green and red bell peppers and cook for 2 to 3 minutes until they begin to soften.
Pour in the crushed tomatoes, diced tomatoes, tomato sauce, and beef broth. Stir everything together.
Add the Italian seasoning, paprika, garlic powder, salt, and black pepper. Stir to combine.
Bring the soup to a boil, then reduce the heat to medium-low. Cover and let it simmer for 20 minutes, stirring occasionally.
Stir in the cooked white rice and let it heat through for 2 to 3 minutes.
Ladle the soup into bowls and top each serving with a generous amount of shredded cheddar cheese and a sprinkle of fresh parsley if desired. Serve immediately.