Heat olive oil in a large skillet over medium heat. Add ground beef, cooking until beef is browned. Drain any excess fat.
Stir in tomato paste, onion powder, garlic powder, paprika, salt, and pepper.
Add gluten-free pasta, beef broth, and milk. Stir well and bring to a simmer.
Cover and cook for 10–12 minutes, stirring occasionally, until pasta is tender.
Remove from heat and stir in shredded cheddar cheese until melted and creamy.
Let sit for 5 minutes before serving.
