Shred the Cheddar and Monterey Jack cheeses from a block and set them aside. Ensure they are near room temperature before incorporating them into the sauce.

Cook and crumble the ground beef in a high-walled pot or Dutch oven over medium-high heat. Drain the grease once browned.

Melt the butter in the same pot and add the minced garlic. Sauté for 1 minute until fragrant.

Add the taco seasoning, Worcestershire sauce, tomato paste, beef broth, chicken broth, whole milk, and Rotel tomatoes with green chilies. Stir to combine thoroughly.

Bring the mixture to a gentle boil. Add the pasta and ensure it is fully submerged in the liquid. Cover and cook according to the pasta package instructions, stirring halfway through.

Remove the cover and check if the pasta is cooked thoroughly. If needed, continue cooking until desired doneness is achieved.

Reduce the heat to low and gradually stir in the cheese until completely melted and smooth.

Let the sauce thicken as it stands, and serve immediately once the desired consistency is reached.