Heat butter in a pot over medium-low heat. Cook and stir onion and jalapeno pepper in the hot butter until onion is translucent, about 5 minutes. Add garlic to onion mixture and cook until fragrant, about 30 seconds.
Whisk chicken broth and cornstarch together in a bowl until smooth; pour into the onion mixture. Cook, stirring constantly, until broth thickens, about 2 minutes. Reduce temperature to low and slowly stir American cheese, 1/4 cup at a time, into broth mixture until cheese is completely melted and sauce is smooth, 5 to 10 minutes.
Stir diced tomatoes, green chile peppers, cumin, and cayenne pepper into cheese sauce and keep pot over low heat. Divide cheese sauce in half, reserving 1/2 of the sauce for another use.
Sprinkle about 1/4 cup Cheddar cheese down the center of 1 tortilla and roll tortilla around cheese. Place rolled tortilla, seam-side down, in a baking dish. Repeat with remaining tortillas and Cheddar cheese. Cover dish with aluminum foil.
Bake in the preheated oven until cheese is melted, 10 to 12 minutes. Remove foil and pour the reserved 1/2 of the cheese sauce over tacos.