Measure all ingredients into a large mixing bowl. With hand held mixer at low speed, beat mixture just until blended. Scrape bowl with spatula a few times. Increase the mixer speed to medium; beat until well blended. Divide dough into 2 portions. Wrap each portion in plastic wrap; refrigerate for 2 hours.
On a lightly floured surface with floured rolling pin, roll half of dough into a 9- x 6-inch rectangle (keep remaining portion in refrigerator). With a sharp knife, cut dough lengthwise into 4 long strips, then cut each strip into 6 1 1/2-inch squares. With dull side of knife, lightly mark a criss-cross design in the shortbread squares, or make other designs. Place cookies, about 1 inch apart, on an ungreased baking sheet. Repeat with remaining dough.
Bake cookies in a preheated 350° oven for 10 to 12 minutes, until lightly browned. Remove cookies to a rack to cool. Store in tightly covered container for up to 1 week.
Makes about 4 dozen cookies.