Adapted from In the Kitchen with a Good Appetite by Melissa Clark.
1. In a small bowl, combine the flour and baking powder. In a food processor or electric mixer with the paddle attachment, mix the butter, salt, and cayenne until creamy. Add 1 cup (4 ounces) of the cheese and mix until thoroughly combined. Gradually add the flour mixture and run the food processor or beat with the paddle until the dough pulls away from the sides of the bowl and starts to form a ball, about 7 minutes. Wrap the dough in plastic, and roll into a log about 1 ½ inches in diameter. Chill in the refrigerator for 1 hour or up to overnight.
2. Preheat the oven to 350˚F and line two sheets pans with parchment. Unwrap the log of dough and slice into rounds 3/16 inch thick. Arrange the rounds on the prepared baking sheets and place a generous pinch of the remaining ½ cup cheese on each cracker. Bake until the crackers are golden brown, about 12 minutes. Turn off the oven and leave the crackers to crisp for an additional 5 minutes. Transfer the crackers to a wire rack to cool.
Variation: Cheddar Hearts or Fishes
Place the dough between 2 sheets of plastic and roll into a rectangle 1/8 inch thick. Using a small (1 ½ to 2 inch) heart- or fish-shaped cookie cutter (I also tried Scotties, which lost their tails, and hand-formed fishes, which look like something a child would make—and eat), cut out the crackers and place them on the prepared baking sheets. Press the remaining scraps of dough together, reroll, and cut out additional crackers, then bake as directed.