Position two oven racks: one of them 1/3 of the way from the bottom and the top rack 1/3 of the way from the top of the oven. Preheat the oven to 350 degrees F.
You'll need at least two (preferably four) UNGREASED noninsulated cookie sheets or sheet pans. You can also cover them with parchment paper (not waxed), if desired. In a medium bowl combine the flour, Clabber Girl Baking Powder and salt. Set aside. In a large bowl with a hand held mixer fitted with beater attachments, beat the butter on low speed until softened. Add the granulated sugar, 1/4 cup at a time, and beat until combined before adding more. Increase the mixer speed to medium and beat for 2 minutes until light in color and creamy. Stop the mixer and scrape the bowl often. Add the egg and vanilla extract and beat on low until incorporated. Add the flour mixture in three equal portions, and fold after each with a large rubber spatula until just incorporated; do not overmix. The dough is very stiff, but not dry.
Pat the dough into a large, 1-inch thick rectangle and wrap it in plastic wrap. Refrigerate the dough, 20 minutes to an hour until well-chilled. This is so the dough will be cold throughout and easier to handle. When chilled, roll out a quarter of the dough on a non-floured surface about 1/8- to 1/4-inch thick; rolling dough in flour is the main culprit in producing hard, dry cookies. Instead, use a Silpat, nonstick mat, but if you don't have one, roll the dough between two pieces of waxed or parchment paper. Keep the unused dough covered in the refrigerator.
Cut cookies from the rolled out dough with cookie cutters. Start from the center out, cutting the cookies close together. Line up the cutter and cut, pressing down firmly to make a clean one. Lift the cutouts with a bench scraper or metal spatula to the cookie sheet and place about 1/2 to an 1-inch apart; don't crowd the baking sheet. This dough spreads about 1/8-inch on all sides.
Don't place cookie dough on a warm cookie sheet because it will cause the cut-out dough to spread and become misshapen. Use one a fresh cookie sheet or one that has cooled thoroughly from the last batch.
If the cookies easily become misshapen, the dough is too warm. Chill the dough you are using to cut the cookies from. Carefully reshape any cookie, if necessary and chill the cut-out cookies on the baking sheet for about 20 minutes before baking. You can bake them right from the refrigerator.
Quickly gather the scraps and press them together to loosely make a flattened rectangular shape without much handling or the cookies will be tough. Re-chill if necessary. For the best texture, avoid handling and re-rolling the scraps too many times. Both actions make a tough dough and cookie from excess gluten development. Bake cookies for 10 to 12 minutes until they just start to take on a light brown color around the edges; do not overbake - the browner the cookies, the harder and more inedible they become. Allow to cool on cookie sheet 1-2 minutes and remove to a wire cake rack to cool. If baked on parchment paper, cookies can be cooled right on its surface. Slide the paper with the cookies on top to a wire cake rack to cool. Remove cookies when cooled.
Use a cold cookie sheet for the next batch.
Recipe by Sarah Phillips, 2004