Preheat oven to 350 degree F. Knead flour into cookie dough. On a lightly floured surface, roll dough into a 13-1/2x9-inch rectangle. Cut into 1-1/2-inch squares. Transfer to ungreased cookie sheets. Bake for 8 to 10 minutes or until edges are firm and tops are browned. Cool on cookie sheets for 1 minute. Remove and cool completely on a wire rack.
Place 1 teaspoon jam or preserves on flat side of 1 cookie. Place a small scoop of ice cream (about 1-1/2 tablespoons) on jam. Top with another cookie, flat side down, and press lightly. Repeat with remaining cookies, jam, and ice cream (there will be extra cookies). Wrap and freeze 4 to 48 hours. Makes 16 sandwiches and 22 extra cookies.