Preheat the oven to 400 degrees F. Line a baking sheet with a silicone baking mat.
Toss together the Cheddar, Parmesan, chili powder, cumin and cayenne in a small bowl.
Spoon heaping tablespoonfuls of the cheese mixture about 1 inch apart on the prepared baking sheet. Spread out each pile and lightly pat down (it's ok if there are gaps). Bake until the cheese is golden brown and bubbly, about 5 minutes.
Let the crisps cool for a few seconds on the baking sheet and then use a metal spatula to lift and drape them over a rolling pin to cool completely. (You can also let them cool on the baking sheet for flat crisps.)
Store at room temperature in an airtight container for up to 2 days.
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