Brown the beef. Heat the olive oil in a large, deep skillet over medium-high heat. Add the ground beef and cook for 5–7 minutes, breaking it into small pieces, until browned. Drain excess grease if necessary.
Cook the onion and garlic. Add the diced onion and cook for 3–4 minutes until softened. Stir in the garlic and cook for about 30 seconds, just until fragrant.
Add the seasonings. Stir in the tomato paste, Italian seasoning, smoked paprika, salt, and black pepper. Cook for 1 minute, stirring well to coat the beef.
Add the pasta and liquids. Pour in the diced tomatoes and beef broth, then stir in the uncooked pasta. Make sure most of the pasta is covered by the liquid.
Simmer until tender. Bring the mixture to a gentle boil, then reduce the heat to medium-low. Cover and simmer for 10–12 minutes, stirring occasionally, until the pasta is al dente. Add a little extra broth if needed.
Make it creamy. Stir in the milk and cook uncovered for 1–2 minutes until the sauce looks creamy and slightly thickened.
Add the cheese. Remove the skillet from the heat. Add the shredded cheddar gradually, stirring until completely melted and creamy.
Rest and serve. Let the cheesy beef pasta skillet rest for 3–5 minutes before serving. Garnish with chopped parsley if desired.