Blend 1 cup flour with sugar. Cut in butter until mixture is crumbly. Add ice cream and blend well. The mixture may firm up because of ice cream; if so continue beating with a wooden spoon or electric mixer to form a dough. Wrap in plastic wrap and refrigerate overnight.
With remaining tablespoon flour, lightly flour board. Remove half of dough from refrigerator and roll out ΒΌ-inch thick. Cut into 3-inch rounds. Place a scant teaspoon of jam in the center of each round. Fold the 2 ends to the center. Place on ungreased cookie sheet. Repeat with remaining dough. Bake in preheated 350- degree oven for 20 to 25 minutes. Cool on cookie sheet 10 minutes, then cool completely before eating. These cookies are best if frozen or eaten within 2 days. Yields about 18 cookies.