Jill, try this recipe. It does make very thin, melt-in-your mouth cookies. Get a huge plastic spatula (mine is 4 inches wide and only used for lifting cookies). Hope that helps. Also be very gentle when removing from cutters...lots of flour.

1-1/2 C. powdered sugar
1 c. butter, softened
1 tsp. vanilla
1/2 tsp. almond extract
1 egg
2-1/2 c. flour
1 tsp. baking soda
1 tsp. cream of tartar

Beat powdered sugar, butter, extracts and egg on medium speed. Stir in remaining ingredients. Cover and refrigerate at least 2 hours. Oven 375 degrees...lightly grease cookie sheets. Divide dough in half and roll on floured surface until 1/4 inch thick (no thinner). Cut with 2-1/2 inch cookie cutters. Place 2 inches apart on sheets. Bake 7 to 8 minutes until edges are light brown. Cool on wire rack. Frost and decorate.

Icing
1 c. powdered sugar
1/2 tsp. vanilla
1 to 2 TBLS milk

Mix.