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Sift together flour, baking powder, and salt in a medium mixing bowl.
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In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and sugar together until light and fluffy, about two minutes. Scrape down the sides and bottom of the bowl and beat for 30 seconds more. Add eggs and vanilla and beat until well combined.
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Gradually add the dry ingredients until just combined, taking care to scrape the dough up from the bottom of the bowl so everything is mixed properly. Divide dough into two portions, pat each portion into a disc, and wrap with plastic wrap. Refrigerate for at least one hour, or overnight.
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Preheat oven to 400 degrees and line two large baking sheets with silicone baking mats or parchment paper.
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Remove half of the dough from the refrigerator and let stand at room temperature for 15 minutes. Lightly dust your workspace with powdered sugar and roll dough out to 1/4-inch thickness. (Alternatively, but less environmentally friendly-ly, roll out dough between sheets of parchment paper.) Cut into desired shapes and place on prepared baking sheets one inch apart. Gather scraps and replace in the refrigerator. Repeat process with other half of dough. Bake until the cookies’ edges are lightly browned, 8 to 10 minutes. Cool completely before making glaze and decorating.