1. Beat together powdered sugar, sugar, butter, oil and eggs until smooth. Add vanilla and almond extract. Gradually mix in baking soda and flour.
2. Cover dough and refrigerate for at least one hour or overnight.
3. Heat oven to 350 degrees F if making 1/4-inch thick cookies or 325 degrees F if making 1/2-inch thick cookies.
4. Remove dough from refrigerator. Dust pastry board with confectioner's sugar. Roll out dough to desired thickness: 1/4 inch for thin cookies or 1/2 inch for thick cookies. Cut in desired shapes with any cookie cutter. Sprinkle with plain or colored sugar if you are not going to ice the cookies. Place 1-inch apart on ungreased cookie sheet and bake 10 to 13 minutes. When done, cookie edges will be lightly browned.
5. If you are in a hurry, shape chilled dough into balls, place 2-inches apart on cookie sheet and flatten with bottom of glass dipped in sugar until about 1/2-inch thick. Bake for 10 to 13 minutes.
5. Let cookies sit on cookie sheet for 2 to 3 minutes before transferring to wire rack. Cool completely. Ice and decorate if desired.