Preheat the oven to 350°. Position 2 racks in the middle and lower thirds of the oven. In a bowl, beat the butter and cheddar at medium speed until combined. Add the flour, cayenne and salt and beat until a crumbly dough forms. Add the rice cereal and beat briefly to combine.
Form level tablespoons of the dough into balls; place on 4 large baking sheets. Using a fork, press a crosshatch pattern into the balls, pressing them into 2-inch rounds.
Bake the crisps 2 sheets at a time for about 25 minutes, until they are lightly browned; shift the pans from top to bottom and front to back halfway through baking for even cooking. Let cool completely.
The crisps can be stored in an airtight container for up to 1 week.