Heat olive oil in a large pot or Dutch oven over medium-high heat. Add the ground beef and diced onion. Cook, breaking up the beef with a spoon, until the beef is browned and the onion is softened, about 5-7 minutes. Drain off any excess grease.

Add the diced bell peppers and minced garlic to the pot. Cook for another 3-4 minutes, stirring frequently, until the peppers begin to soften and the garlic is fragrant.

Stir in the dried oregano, smoked paprika, and optional red pepper flakes. Cook for 1 minute more to toast the spices.

Pour in the crushed tomatoes, undrained diced tomatoes, beef broth, and Worcestershire sauce. Add the optional brown sugar. Stir everything together and bring the soup to a boil.

Once boiling, reduce the heat to low, cover the pot, and let it simmer for 20 minutes to allow the flavors to meld.

Stir in the uncooked rice. Return the soup to a simmer, then cover and continue to cook for another 15-20 minutes, or until the rice is tender. Stir occasionally to prevent the rice from sticking to the bottom of the pot.

Taste the soup and season generously with salt and black pepper as needed. Stir in most of the fresh parsley, reserving some for garnish. Ladle into bowls and top with shredded cheese and remaining parsley, if desired.