In a large pot, heat olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes. Add the minced garlic and cook for an additional minute until fragrant.
Add the ground beef to the pot, breaking it apart with a spoon. Cook until browned and fully cooked, about 7-10 minutes. Drain excess fat if necessary.
Stir in the chopped cauliflower, beef broth, thyme, paprika, salt, and pepper. Bring the mixture to a boil, then reduce heat to low. Cover and simmer for 15-20 minutes, or until the cauliflower is tender.
Once the cauliflower is tender, use an immersion blender to puree the soup until smooth. If you don’t have an immersion blender, carefully transfer the soup in batches to a regular blender.
Stir in the softened cream cheese until fully incorporated and creamy. Adjust seasoning with more salt and pepper if needed.
Serve hot, garnished with fresh parsley.