Make the Base Sugar Cookie Dough: Whisk the flour, baking powder, and salt in a bowl.
Beat the butter and sugar in a stand mixer fitted with the paddle attachment until fluffy and creamy, stopping the mixer and scraping down the sides midway if you have to, 3–4 minutes. Stop the mixer, then add the eggs and vanilla, return to medium speed and beat until creamy, 2 minutes. Stop the mixer, add the dry ingredients, then turn on the mixer to low and beat until everything is incorporated, being careful not to overwork the dough. Divide the dough into three equal-sized pieces.
Make the Spice Cookies: Take one piece of dough and before chilling, add ½ teaspoon ground cinnamon, ½ teaspoon ground ginger, and ⅛ teaspoon each ground cayenne and ground nutmeg (you can do this in the stand mixer or by hand). Wrap the dough in plastic wrap and chill for 1 hour.
Roll each piece into a ball, and then roll the cookies in the sugar mixture. Arrange three inches apart on parchment-lined baking sheets and press with the center of your palm into a 2-inch round. Bake until lightly golden around the edges, 10–11 minutes. Cool completely. Store in an airtight container for up to four days.