Beat butter at medium speed with an electric mixer until creamy; gradually add powdered sugar, beating well. Add vanilla, beating until blended.
Combine flour, baking powder, and salt; add to butter mixture, beating at low speed until blended.
Divide cookie dough in half; shape each portion into a 10-inch log. Wrap in wax paper, and chill 8 hours; or freeze up to 6 weeks, and thaw in refrigerator.
Cut each roll into 1/3-inch-thick slices; place on lightly greased baking sheets.
Bake at 350º for 10 to 12 minutes or until lightly browned. Transfer to wire racks to cool.
Chocolate-Dipped Shortbread Cookies: Microwave 1/2 cup semisweet chocolate morsels in a glass bowl at HIGH 1 minute. Stir until smooth. Dip half of each cooled cookie into chocolate. Place on wax paper to set.
Peanut Butter-and-Jelly Shortbread Cookies: Stir 1/2 cup peanut butter into dough after adding flour mixture. Make an indentation in center of each cookie slice before baking. Fill each indentation with 1/4 teaspoon jelly.
Chocolate-Mint Shortbread Cookies: Stir 1 (67-ounce) package chocolate mints, chopped, into dough after adding flour mixture. Proceed as directed.
Toffee Shortbread Cookies: Stir 1 cup almond brickle chips into dough after adding flour mixture. Proceed as directed. (For testing purposes only, we used Heath Bits o' Brickle chips, found near chocolate chips in the grocery store.)
Pecan-Crusted Shortbread Cookies: Coat #10-inch logs with 3/4 cup finely chopped pecans. Proceed as directed.
Red Cinnamon Candy Shortbread Cookies: Stir 1/2 cup red cinnamon candies into dough after adding flour mixture. Proceed as directed.
Snowman Shortbread Cookies: Chill dough 2 hours after adding flour mixture. Shape dough into 16 (3/4-inch) balls, 16 (1/2-inch) balls, and 16 (1/4-inch) balls. Use 1 ball of each size to make snowman shapes, leaving no space between balls. Bake as directed. For eyes, use black gel frosting after cookies cool, or press chocolate mini morsels onto warm cookies. Make scarves using red decorator frosting after cookies cool.