Place room-temperature butter, (salt if unsalted butter) and 1 cup of 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.