Heat a large deep skillet over medium heat and add the olive oil. When shimmering, add the chopped onion and sauté 3–4 minutes until softened. Stir in the minced garlic and cook 30 seconds more until fragrant.
Increase heat to medium-high, add the ground beef to the pan, and break it up with a spatula. Season with salt, pepper, paprika, and chili powder. Cook 6–8 minutes until no longer pink, stirring occasionally. If excess fat accumulates, carefully drain or blot some from the pan.
Push the beef to one side of the skillet and add the tomato paste to the empty space. Let it cook 1 minute, stirring the paste until it darkens slightly (this concentrates the flavor), then mix it through the meat.
Pour in the beef broth and Worcestershire sauce to deglaze the pan, scraping up any browned bits from the bottom. Stir in the milk, then add the dry pasta, distributing it in an even layer.
Bring the mixture to a gentle boil, then reduce heat to medium-low. Partially cover the skillet and simmer, stirring every few minutes to prevent sticking, until the pasta is al dente and most of the liquid has been absorbed, about 10–12 minutes (cooking time varies by pasta).
Remove the pan from the heat and sprinkle the shredded cheddar over the top. Cover the skillet and let rest 3–4 minutes to allow the cheese to melt and the sauce to thicken. Stir gently to create a creamy, even sauce.
Taste and adjust seasoning with extra salt or pepper if desired. Serve hot garnished with chopped parsley.