Mince the garlic cloves and shred the cheddar and Monterey Jack cheese from blocks (freshly shredded cheese melts much more smoothly than pre-shredded varieties). Cut the Velveeta into ½-inch cubes. In a large pot or Dutch oven over medium-high heat, brown the ground beef, breaking it apart as it cooks until no pink remains, about 5-7 minutes. Drain excess grease, leaving just a thin coating in the pot.

Add the butter to the pot with the cooked beef and let it melt over medium heat. Add the minced garlic and cook for about 1 minute until fragrant. Stir in the tomato paste and cook for another minute to caramelize it slightly, which deepens the flavor. Add the taco seasoning, Worcestershire sauce, and smoked paprika, stirring well to coat everything and bloom the spices.

Pour in the beef broth, chicken broth, and milk, stirring to combine and scraping up any browned bits from the bottom of the pot. Add the canned tomatoes with green chilies (with their liquid). Increase heat to medium-high and bring the mixture to a rolling boil, stirring occasionally.

Once boiling, add the medium pasta shells and stir well to prevent sticking. Return to a boil, then reduce heat to medium-low and partially cover the pot (leave the lid slightly ajar so the liquid doesn't boil over). Cook for about half the package time, then stir the pasta, breaking up any clumps that have formed. I like to cook the pasta slightly under al dente here since it will continue cooking as the sauce thickens.

Continue cooking for the remaining time until the pasta is just tender and most of the liquid has been absorbed (the mixture should still be creamy but not soupy). The pasta should be at or slightly below al dente—remember it will continue to soften as it cools slightly. Stir occasionally to ensure even cooking.

Remove the pot from heat or reduce to the lowest setting. Add the shredded cheddar, Monterey Jack, and Velveeta cubes from Step 1, stirring constantly and gently until completely melted and incorporated, about 2-3 minutes. The Velveeta cubes melt faster than block cheese and help create a silky, cohesive sauce. If the sauce seems too thick, add a splash of milk to reach your desired consistency. Let it rest for 2-3 minutes before serving—the residual heat will help the sauce thicken to the perfect creamy texture.