In a large bowl, beat the butter until creamy. Add the sugar and beat until combined. Beat in the egg whites, 1 at a time, then beat in the flour. Refrigerate the dough until firm, if necessary. Divide the dough in half and transfer to 2 large sheets of plastic wrap. Shape the dough into 2-inch-thick logs, and wrap in the plastic. Refrigerate until firm, at least 2 hours.
Preheat the oven to 350°. Using a sharp, thin knife, slice 1 log of dough 1/4 inch thick. Arrange the cookies 2 inches apart on 2 large cookie sheets. Bake the cookies on the middle and lower racks of the oven for about 17 minutes, or until golden at the edges, shifting the pans from top to bottom and back to front halfway through. Let the cookies cool on the sheets for 5 minutes, then transfer them to wire racks to cool completely. Wipe the cookie sheets clean and let cool completely, then repeat with the second log of dough.
The cookies can be stored in an airtight container at room temperature for up to 1 week or frozen for up to 2 months.