Using an electric mixer on medium speed, beat together the cheese and butter until fluffy, about 3 minutes. Reduce the mixer speed to low and mix in the salt, cayenne, black pepper, and garlic powder. Using a rubber spatula, stir in the flour ½ cup at a time, until the ingredients are well combined and a dough forms.
Turn the dough out onto a piece of parchment paper or plastic wrap and shape it into a 1-inch-diameter log. Twist the ends of the parchment or plastic wrap to seal. Refrigerate for 30 minutes.
Preheat oven to 375 degrees F. Line a baking sheet with parchment paper or a silicone baking mat.
Remove the dough from the refrigerator, unwrap, and place on a cutting board. Cut the log into ⅛-inch-thick slices and place ¼ inch apart on the prepared baking sheet.
Bake until light golden brown, about 15 minutes. Transfer the pan to a wire rack and allow the crackers to cool completely. The crackers can be stored in an airtight container at room temperature for up to 1 week.
Notes
If the dough seems to stiff or dry, gradually add 1 to 2 tablespoons of ice water until it reaches the right consistency.
You can store the unbaked cracker dough in the refrigerator for up to 1 week before baking. It can also be stored in the freezer for up to 2 months - just place the wrapped dough in a resealable freezer bag.