In a large, deep skillet over medium-high heat, brown the ground beef, breaking it up, until it has dark, crispy bits. No need to drain with lean beef.
Lower the heat to medium. Stir in the tomato paste, dried minced onion, dried minced garlic, chili powder, smoked paprika, cumin, oregano, salt and pepper. Cook, stirring constantly, about 2 minutes, until the paste darkens slightly and the spices are fragrant.
Add the beef broth, milk, tomato sauce and Worcestershire, scraping up the browned bits. Raise the heat to medium-high and bring to a simmer.
Stir in the elbow noodles, reduce the heat to low, cover and cook about 18 minutes, until tender, stirring every few minutes.
Remove from the heat and stir in the cheddar until melted. Taste and adjust salt and pepper. Let rest 5 minutes before serving.