Cream the Butter - In a stand mixer fitted with the paddle attachment, add the softened butter and sugar. Mix on medium-low speed (setting 4) until light and fluffy, 2 minutes. Scrape down the sides of the bowl with a spatula.
Incorporate the Egg - Add the room temperature egg, lemon zest (if using), and vanilla extract. Mix on medium-high speed (setting 6) until combined, 20 to 30 seconds. Scrape down the paddle, side, and bottom of the bowl.
Add the Dry Ingredients - Sift the flour and baking powder into a medium bowl. Add the salt, whisk to combine, then add to the mixer. Pulse on and off 8 times. Scrape down the sides of the bowl. Mix on low speed (setting 2) until the dough just comes together, 10 to 15 seconds. Do not overmix. Use a spatula to give a final mix.
Refrigerate the Dough - Transfer half of the dough to a piece of plastic wrap, cover, and press into a ½" thick disc. Repeat with the remaining dough. Refrigerate for at least 1 hour, 3 hours is ideal. Alternatively, freeze for 30 to 90 minutes.
Preheat the Oven - Set the oven rack to the middle position. Heat to 350ºF (177ºC). Line two baking sheets with parchment paper, then set aside.
Roll Out the Dough - Work with one piece of dough at a time to keep it cool. Allow the dough to sit on the counter for 5 to 10 minutes to make it easier to roll. Lightly dust the work surface, the top of the dough, and the rolling pin with flour, using more as needed as the dough is slightly sticky. Roll, rotate, and dust with flour until ¼" thick.
Cut Out Shapes - Immediately use desired cookie cutters to cut out shapes, cutting them as close together as possible. Transfer the pieces to the parchment paper lined sheet pans, about 1" apart. Any extra dough scraps can be rerolled out 1 more time. If needed, chill before rolling.
Bake - Bake the cookies while still cool, one tray at a time. If not baking immediately after cutting, keep them chilled in the refrigerator. Bake for 6 minutes, rotate, and bake for an additional 4 to 5 minutes, or until the surface is dry and the bottoms are lightly golden brown.
Cool - Cool on the baking sheet for 3 to 5 minutes, then transfer cookies to a wire rack. Alternatively, for a softer cookie with less crisp edges, immediately transfer to the wire rack. Completely cool the cookies before decorating, about 30 minutes.
Repeat Process - Roll out the remaining piece of dough and repeat the cutting and baking process. If reusing the parchment paper lined sheet pans, make sure the pan is cooled down before using.
Notes
Properly weigh the flour: Weigh the flour on a digital scale for the most accurate results. Alternatively, dip the measuring cup into the flour, then sweep off the excess flour. This makes for a denser measurement, but don’t pack the flour in the cup.
Bake time: About 10 minutes for 2-inch cookies, 11 minutes for 3-inch cookies, or 12 minutes for 4-inch cookies. A visual check will be the best guide.
Baking a smaller batch: If baking only about 6 cookies on a tray, check for doneness sooner. After baking for 6 minutes and rotating, check every 1 minute. They brown much faster due to less moisture in the environment.
Make-ahead dough: The dough can be mixed and stored refrigerated for up to 5 days, or 1 month frozen. Unbaked cut-out cookies can be covered and refrigerated for up to 5 days, or frozen for 2 weeks.
Storing: Store baked cookies in an airtight container for up to 7 days at room temperature. Store in the freezer for up to 3 months.