Shred the Cheddar and Monterey Jack from a block and set them aside before you begin cooking. The cheese should be closer to room temperature than fridge-cold so it melts into a smoother sauce.
Cook and crumble the ground beef in a high-walled pot or Dutch oven over medium-high heat, then drain off the grease. The beef should be browned with no large pink pieces left, and draining keeps the finished pasta from tasting oily.
Melt the butter in the same pot, then add the minced garlic and cook for 1 minute. You should hear a gentle sizzle and smell the garlic bloom in the butter without letting it brown too far.
Stir in the taco seasoning, Worcestershire sauce, tomato paste, beef broth, chicken broth, whole milk, and Rotel tomatoes with green chilies, keeping the pasta and cheeses out for now. The liquid should look well mixed and lightly reddish with the tomato paste fully worked in.
Bring the mixture to a gentle boil, add the pasta shells, and press them under the liquid. Once covered, the pasta should cook according to the package directions while gentle bubbling continues across the surface.
About halfway through cooking, run a silicone spatula along the bottom of the pot to loosen anything that may be settling. This keeps the shells from sticking, and the mixture should stay saucy rather than scorched or clumpy.
Remove the lid and taste a shell to check doneness, covering again briefly if the pasta needs more time. The shells should look plump and have absorbed most of the liquid while a good amount of sauce still remains.
Lower the heat and stir in the cheeses a little at a time until fully melted. The sauce should turn creamy and glossy as the cheese disappears instead of forming grainy bits.
Let the pasta stand briefly, then serve when the sauce reaches the consistency you like. It will continue to thicken as it sits, so a slightly loose sauce in the pot is exactly where you want it.