Heat olive oil in a large pot over medium heat. Add ground beef and cook until browned, breaking it up with a spoon. Drain excess fat if needed.
Stir in diced onion, garlic, carrot, and celery. Cook for 4-5 minutes until vegetables are softened.
Add beef broth and bring to a boil. Add elbow macaroni and reduce heat to simmer. Cook for 8-10 minutes, stirring occasionally, until pasta is al dente.
In a small bowl, whisk together milk, heavy cream, and flour until smooth. Slowly pour this mixture into the pot, stirring continuously to avoid lumps. Simmer for 2-3 minutes until soup thickens slightly.
Stir in shredded cheddar and mozzarella, smoked paprika, mustard powder, salt, and pepper. Stir until the cheese melts completely and the soup is creamy.
Ladle the soup into bowls, garnish with fresh parsley if desired, and serve warm with crusty bread or crackers.
