In a large pot or Dutch oven, heat the oil over medium-high heat. Add the onion, bell peppers, and garlic and cook, stirring, until tender, about 5 minutes.
Add the beef and the Italian sausage and cook, breaking up the meat with the edge of a wooden spoon, until cooked through or no longer pink, about 5 minutes. Drain off excess fat.
Add the tomato paste, salt, pepper, and red pepper flakes and stir until well combined. Pour in the diced tomatoes, tomato sauce, beef broth, oregano, basil, and parsley. Bring soup to a rapid simmer.
Reduce the heat to a light simmer, cover and let cook to allow the flavors to mend, 15 to 20 minutes.
To serve, add about ¼ cup of raw, riced cauliflower to the bottom of a serving bowl (if using). Ladle the hot soup over the riced cauliflower. Garnish with more parsley or basil, if desired.