Recipe courtesy of The Martha Stewart Show. Step 1 Sift flour, baking powder, and salt into a bowl. Step 2 Put butter and sugar in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until pale and fluffy. Mix in eggs and vanilla. Reduce speed to low.
Cream butter with 1 cup powdered sugar and 1 cup granulated sugar. Beat in eggs until smooth. Slowly stir in oil, vanilla, baking soda, cream of tartar, salt and flour. Chill for easy handling. Shape into walnut-size balls. Dip in sugar. Place on baking sheet and press down with the bottom of a glass. Bake at 350 degrees 10 to 12 minutes.
Using 2-1/2-inch cookie or biscuit cutters, cut into desired shapes. Place 1 inch apart on ungreased cookie sheet. Bake in a 350 degrees F oven for 7 to 9 minutes or until edges are firm and bottoms are very lightly brown. Transfer to a wire rack; cool completely.
Sift flour, baking powder, and salt into a bowl. Put butter and sugar in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until pale and fluffy. Mix in eggs and vanilla.