Preheat your oven to 400°F. Line two large baking sheets with parchment paper or silicone baking mats.
In a bowl, toss together the shredded cheddar, pepper jack, chili powder, cumin, smoked paprika, garlic powder, onion powder, and cayenne until the cheese is evenly coated in the spices.
Drop tablespoon-sized mounds of the seasoned cheese onto the prepared baking sheets, spacing them about 2 inches apart. Press each mound flat with your fingers or the back of a spoon into thin, even rounds.
Bake for 7 to 9 minutes, watching carefully, until the edges are dark golden brown and the cheese has stopped bubbling in the center.
Let the crisps cool completely on the baking sheets. They will transform from flexible and oily to perfectly crunchy and snackable as they cool. These taste remarkably like nacho cheese tortilla chips.