Stir flour mixture into wet ingredients in batches, mixing well after each addition. Chill dough for 30 minutes.
While dough chills, whisk together the powdered sugar and milk to create a thin icing (adding vanilla if desired) and set aside.
1 cup sifted powdered sugar, 2 tablespoons milk, 1/2 teaspoon pure vanilla extract
Fit chosen disc to cookie press and screw into bottom. Fill press barrel with about 1 cup of dough, screw on top, and press trigger until dough reaches the disc.
Set press bottom onto cookie sheet and press trigger to push out a cookie, then lift straight up. The cookie should stick to the pan. (You may need to do a few "primer" cookies to get it ready.) Repeat with remaining dough, leaving about 1 inch between cookies.
Bake cookies for 6-8 minutes, then let cool on the pan for 5 minutes. Dip each cookie into the icing, let the excess drip off, then place on a wire rack to cool completely.
Notes
Chill remaining unshaped dough while cookies bake.
If you can, swap your baking sheets between bakes so that you are not piping onto a hot pan.