Place room-temperature butter, (salt if unsalted butter) and granulated sugar in stand mixer with paddle attachment and mix on low until smooth. Creamed butter should be fluffy and pale yellow in color.
Add 1 large egg at room temperature and mix on medium (4 on Kitchenaid mixer) in stand mixer until fully incorporated. Scrape bowl when necessary to make sure egg incorporates.
Add 1 tsp of vanilla extract. Mix until just incorporated.
In a separate bowl, whisk dry ingredients (AP flour, baking powder, nutmeg) together.
Add dry ingredients into stand mixer with a scoop (about 1/3 of total dry ingredients at a time) and mix until fully incorporated. Start mixer on slow until flour starts to incorporate, then turn up to medium. Scrape bowl as needed to fully incorporate.
Add 1 tsp of milk once flour is fully incorporated. Continue to mix on slow until dough becomes a solid mass.
Scrape out mixer bowl, wrap up sugar cookie dough in plastic wrap and chill in refrigerator for 2 hours.
Knead cookie dough and roll out cookie dough until thin to cut cookie shapes. Use a cookie cutter to cut out uniform shapes.
Place cookies on a baking sheet lined with parchment paper. Put cookie sheet back in refrigerator for about 15 minutes to chill again.
Bake chilled cookies at 350ºF for 10-14 minutes depending on size of cookie. Cookies will be slightly golden brown on the edge. Chilled cookie dough will keep it's shape in the oven and not expand or warp.