Whisk the flour, baking powder, and salt in a medium bowl.
Beat the butter and both sugars in another medium bowl with an electric mixer on medium-high speed until light and fluffy, about 30 seconds. Add the eggs and vanilla mixing until fully incorporated. Slowly add the flour mixture, and continue beating just until the dough comes together, stopping and scraping down the sides of the bowl as needed.
Divide dough in half, pat into disks, wrap in plastic wrap and refrigerate until firm, at least 2 hours.
Generously flour a clean work surface. (For a nice, even layer of flour, lightly sift flour over the work surface.) Gently roll chilled dough about 1/4-inch thick. Cut into desired shape using a cookie cutter, working quickly enough so dough remains chilled. If dough gets too soft, refrigerate on a lined baking sheet until firm again, about 30 minutes.
Transfer cut cookies to un-greased baking sheets, leaving about 1-inch between cookies. Refrigerate the formed cookies for at least 30 minutes. Lightly dust off excess flour with a dry pastry brush. (Excess dough can be pressed into a disk, chilled and rerolled.)
Preheat the oven to 325 degrees F. Bake the cookies, until the bottoms are golden, about 12 to 15 minutes depending on shape. Cool on the baking sheets until firm enough to transfer to a rack to cool. Decorate as desired and serve. Store in an airtight container at room temperature for up to 1 week.
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