Heat a double boiler over medium heat. Once the water is boiling, add half-and-half, cumin, garlic salt, white American cheese pieces, shredded Monterey Jack cheese, chopped green chiles, and diced tomatoes with green chile peppers, respectively, to the bowl of the double boiler; cook, stirring often, until the cheeses are melted and the mixture is smooth, about 15 minutes.
Stir spinach into melted cheese mixture; heat until the spinach wilts, 5 to 10 minutes.