Preheat the oven to 350° and position a rack in the upper and lower third. In a medium bowl, using a handheld electric mixer, beat the butter with the Parmesan and flour at low speed until a stiff dough forms. Divide the dough into 3 pieces, then roll each piece into a 9-inch log, about 1 1/2 inches in diameter.
Slice the logs 1/3 inch thick and arrange the slices on 2 large, nonstick baking sheets. Bake for 18 minutes, or until golden, shifting the pans halfway through baking for even browning. Let the cookies cool for 10 minutes, then transfer them to a wire rack to cool completely.
The cookies can be stored in an airtight container for up to 5 days.