Bring a pot of salted water to a boil and cook the elbow macaroni according to the package directions. Drain and set aside.
Heat a large pot over medium-high heat. Add a little oil if needed, then cook the ground beef while breaking it into small crumbles.
Once the beef is almost cooked through, add the diced onion and minced garlic. Season lightly with salt and black pepper, then cook for a few more minutes until the onion softens and the garlic becomes fragrant.
Lower the heat to medium. Pour in the evaporated milk and whole milk, then add the cubed Velveeta and freshly grated sharp cheddar.
Heat gently until the cheese melts into a smooth sauce and the milk reaches a light simmer. Do not let the mixture come to a hard boil.
Turn off the heat, add the drained macaroni, and stir until the pasta and ground beef are evenly coated in the cheese sauce.
Taste and adjust the salt and black pepper as needed. Serve while hot and creamy.