In the bowl of a stand mixer fitted with the paddle attachment, cream the softened butter on high speed until it is light and fluffy— about 2 minutes.
Next, add the powdered sugar, vanilla extract, cinnamon, nutmeg, and salt. Mix on low speed just until it is all combined— about 1 minute.
Next, with the mixer on low speed, alternate between adding the flour and milk in two batches. First, add half of the flour, then half of the milk, then the remaining half of flour, and finally the remaining half of milk.
Allow the mixer to continue on low speed until the dough comes together in a ball around the paddle.
Shape the dough into a disk and wrap it in plastic wrap. Refrigerate for 15 minutes.
While the dough rests, preheat your oven to 375F and line a baking sheet with parchment paper.
Once the dough has chilled, lightly flour your work surface and roll out the dough until it is 1/4” thick.
Using a 2” cookie cutter, cut out 12 circles of dough and place them 1” apart on the baking sheet. Note: Make sure to flour the cookie cutter so the dough doesn’t stick.
Bake for 10-12 minutes, or until the edges of the cookies are just starting to turn golden brown. Allow the cookies to cool to room temperature on the tray.