Grate the cheese and the cold butter together in a food processor. Switch from the grating blade to the metal blade, then add the flour, salt, paprika, Worcestershire sauce, and cayenne pepper. Process until the dough just begins to come together and looks moist and grainy. With the motor running, drizzle in the buttermilk until the dough begins to pull away from the sides and form a ball.
Cut two lengths of waxed paper, divide the dough into two portions, and place each one on a waxed paper length. Form these into two logs and roll them tightly, pressing in to form nice solid logs. Twist the ends like a candy wrapper. Refrigerate the logs for at least an hour before baking, but you can refrigerate them for 2 days or freeze them for 3 months.
When ready to bake, preheat the oven to 350°F and line two baking sheets with parchment paper. Remove the rolls from the fridge and slice into medium-thick wafers, about ¼ inch each. Flatten with the tines of a fork, if desired, for decoration. Or, top with a pecan half.
Place them on the baking sheet with a little room to spread, and bake until golden around the edges and firm on the top, about 10 to 12 minutes. Cool on the pans for a few minutes, then remove to wire racks to cool.