In a large bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking powder, and salt; beat until combined, scraping side of bowl occasionally. Add oil, egg, and vanilla; beat until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour. Divide dough in half. Cover and chill for 1 to 2 hours or until easy to handle.

Preheat oven to 375 degrees F. On a lightly floured surface, roll dough, half at a time, to an 1/8-inch thickness. Using a 2-1/2-inch cookie cutter, cut into desired shapes.* Place cutouts 1 inch apart on ungreased cookie sheets. Reroll scraps as necessary.

Bake for 6 to 8 minutes or until edges are firm and just starting to brown. Transfer to a wire rack; cool. Makes about 48 cookies.

Choose from Splenda Sugar Blend for Baking or Equal Sugar Lite. Follow package directions to use product amount equivalent to 1/2 cup sugar.PER COOKIE WITH SUBSTITUTE: same as above, except 44 cal., 5 g carbo.Carb Choices: 0

Nutrition facts are based on 1 cookie.

To make holes in cookies for hanging, use a drinking straw to cut holes in cookies before baking.