Preheat oven to 350°F. In a medium bowl, add flour, baking powder, and salt (measuring the flour with a food scale is the most accurate, but not required). Whisk to combine and remove any lumps. Set aside.
In a large bowl, add butter and sugar. Beat with an electric mixer for 3 minutes. Add the egg and vanilla and beat for another minute. With the mixer on low, gradually add the flour mixture. Mix until the dough begins to pull away from the sides of the bowl. Transfer the dough to a large piece of parchment paper and knead by hand for a few minutes. Divide the dough in half and wrap each portion in parchment. Chill in the refrigerator for about 30 minutes.
To roll the dough, place another sheet of parchment on top and roll with a rolling pin until ⅛–¼ inch thick. Cut into 2.5" shapes and remove the excess dough, leaving the cut shapes in place. Gently slide the parchment with the cookies onto a baking sheet with raised edges, such as a half sheet pan. Repeat for remaining dough. Bake for 9–11 minutes, or until the edges are slightly golden. Let cool completely. Store cooled sugar cookies in an airtight container at room temperature for up to 1 week.
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Notes
For longer storage, freeze undecorated cookies in a freezer-safe container or bag for up to 3 months. Thaw at room temperature before decorating or serving.