In the bowl of an electric mixer fitted with the paddle attachment, beat together the butter, sugar, and salt until the mixture is creamy, scraping down the sides of the bowl as needed. Mix in the vanilla.
In a separate bowl, whisk together the flour and spices, then add to the mixer bowl, mixing on low. The mixture will be crumbly. Add the milk and beat until a dough forms. Divide the mixture into two and pat into disks. Wrap in plastic wrap and refrigerate for at least 1 hour.
Preheat the oven to 350ºF. Line two cookie sheets with parchment paper. Working with one disk at a time, roll out the dough on a lightly floured surface and cutout shapes with cookie cutters. Place on prepared baking sheets, spacing 1 inch apart. Bake until the edges just begin to turn golden brown, about 14 minutes.
Let cool slightly before transferring to a rack to cool completely. Repeat with remaining dough and rerolling scraps.