Preheat the oven to 325 degrees F (165 degrees C). Lightly grease a large cookie sheet.
In a medium bowl, mix together the flour, salt and cayenne pepper. Stir in the Cheddar cheese and melted butter to form a firm dough. Roll pieces of dough into ropes as big around as a penny. Slice into 1/4 inch slices. If dough is too soft, it can be chilled until firm. Place slices onto the prepared cookie sheet so they are 1 inch apart.
Bake for 20 to 25 minutes in the preheated oven, until the bottoms of the pennies are lightly toasted and the tops are firm. Allow to cool completely before serving. Store in an airtight container at room temperature.