Heat a large deep skillet or Dutch oven over medium-high heat. Add the ground beef and diced onion, then cook for 6 to 8 minutes, breaking the beef into small pieces, until the meat is browned and the onion is softened. Drain excess fat if necessary.

Add the minced garlic and cook for about 30 seconds, stirring constantly. The garlic should smell fragrant without becoming deeply browned.

Stir in the tomato paste, flour, paprika, Italian seasoning, kosher salt, black pepper, and Worcestershire sauce. Cook for 1 minute so the flour and tomato paste lose their raw taste and coat the beef.

Gradually stir in the low-sodium beef broth and whole milk while scraping the browned bits from the bottom of the skillet. Continue stirring until the liquid is smooth and the seasoned beef is evenly distributed.

Bring the mixture to a gentle boil, then stir in the uncooked noodles. Reduce the heat to medium-low, cover the skillet, and simmer for 8 to 12 minutes, stirring occasionally, until the noodles are tender.

Remove the skillet from the heat and stir in the freshly shredded sharp cheddar until melted and creamy. Let the beef noodles stand for 2 to 3 minutes before serving so the sauce can thicken.