In a large pot or Dutch oven over medium heat, brown the ground beef along with the diced onion until the meat is cooked through, about 5-7 minutes. Drain any excess fat if necessary.
Add the minced garlic and cook for an additional 1-2 minutes until fragrant.
Stir in the cauliflower florets, beef broth, dried oregano, salt, and black pepper. Bring the mixture to a boil.
Once boiling, reduce the heat to low, cover, and let it simmer for about 20 minutes, or until the cauliflower is tender.
If you prefer a smoother texture, use an immersion blender to blend the soup to your desired consistency. If you like it chunky, you can skip this step.
Stir in the heavy cream and let the soup simmer for another 5 minutes, allowing the flavors to meld.
Serve hot, topped with shredded cheddar cheese and garnished with fresh parsley if desired.