Place the cubed white American cheese, half-and-half, and butter in a medium saucepan over low heat. Stir continuously until the cheese melts completely and the mixture is smooth.
Stir in the jalapeños, ground cumin, garlic powder, onion powder, and a pinch of cayenne pepper. Adjust the seasoning as needed. If you prefer a thinner dip, slowly add the optional milk until you reach your desired consistency.
Remove the saucepan from the heat and serve the dip warm with tortilla chips or your favorite dippers.