Place American cheese and about 1/4 cup half-and-half in a saucepan over low heat; cook and stir until cheese starts to melt, about 5 minutes. Slowly start stirring half-and-half into cheese mixture, about 2 tablespoons at a time, until cheese begins to melt and mixture is smooth, about 5 minutes more. Continue adding more half-and-half.
Season cheese mixture with cumin, black pepper, and salt; add red pepper flakes, a little at a time, until desired spiciness is reached.
Cook and stir cheese dip until cheese is fully melted, adding more half-and-half if needed to thin it out, 5 to 10 minutes more. Remove from heat and top dip with chili powder.