Heat a large Dutch oven or soup pot over medium heat. Add the olive oil only if the ground beef is very lean, then add the beef and diced onion. Cook for 6–8 minutes, breaking the beef into small pieces, until browned and the onion is tender.

Drain excess fat from the pot if necessary. Add the minced garlic and cook for about 30 seconds, stirring constantly, just until fragrant.

Add the cauliflower, undrained diced tomatoes, tomato sauce, beef broth, Italian seasoning, kosher salt, black pepper, and optional paprika. Stir well to distribute the seasonings and vegetables.

Bring the soup to a boil over medium-high heat. Once bubbling, reduce the heat to medium-low and partially cover the pot.

Simmer for 20–25 minutes, or until the cauliflower is fork-tender. Avoid prolonged boiling so the cauliflower keeps its shape instead of breaking apart into the broth.

Taste the soup and adjust the salt and pepper as needed. Ladle it into bowls, garnish with chopped fresh parsley, and serve hot.