Heat your large skillet over medium-high heat. Add the ground beef and break it up with a wooden spoon. Season generously with a pinch of salt and pepper. Once the beef is about halfway browned, toss in the diced yellow onion. Continue cooking until the beef is fully browned and the onion is translucent, about 6 to 8 minutes. If you used 80/20 beef, drain off any excess grease now.

Reduce the heat to medium. Push the beef and onions to one side and add the minced garlic to the cleared space, cooking for about 60 seconds until fragrant. Then, sprinkle the flour, chili powder, and smoked paprika evenly over the meat mixture. Stir well for about 2 minutes to prevent separation and add deep flavor.

Pour in the water (or beef broth) and the milk. Stir the bottom of the skillet well, scraping up any browned bits on the bottom for added flavor. Stir in the tablespoon of ketchup or tomato paste. Bring the mixture to a low boil.

Once the liquid is simmering comfortably, add the uncooked elbow macaroni. Stir well and ensure the pasta is mostly submerged. Reduce the heat to low, cover the skillet tightly, and let it simmer for 10 to 12 minutes, or until the pasta is tender (al dente). Stir it halfway through to prevent sticking. The liquid should have thickened significantly as the pasta absorbed it.

Remove the skillet from the heat to ensure a silky, non-grainy sauce. Stir in half of the sharp cheddar cheese until it is entirely melted and incorporated, creating a rich, luscious sauce that binds everything together.

Taste and adjust seasoning with salt and pepper if needed. Sprinkle the remaining cheddar cheese evenly over the top of the skillet. Place the lid back on for 2-3 minutes to melt the cheese purely with residual heat, or pop the whole oven-safe skillet under the broiler for 1 to 2 minutes until the cheese is bubbling and slightly golden for a delightful, crispy top layer. Let it rest for five minutes before serving.