Whisk the dry ingredients except the sugar. In the bowl of an electric mixer fitted with a paddle, cream the butter with the sugar until slightly fluffy. Slowly beat in the milk.
On low speed, beat in the dry mixture until combined; dough will be sticky. Divide the dough into 4 equal portions, roll each to 1/4 to 1/8-inch thick between sheets of parchment paper, and freeze until firm, about 20 minutes.
Preheat the oven to 325 degrees F. Line sheet pans with parchment paper.
Put the cookie dough on a floured work surface; cut and transfer cookies to the prepared sheets. Reroll and cut the scraps into cookies.
Bake the thinner cookies for about 11 minutes, until crisp, and the thicker about 20 minutes. Cool for about 2 minutes, then transfer to a rack to finish cooling.