Heat oven to 400°F.
Place 1 cup butter into bowl; beat at medium speed 30 seconds. Add sugar, pumpkin pie spice, baking soda and salt; continue beating, scraping bowl occasionally, until well mixed. Add egg and 1 teaspoon vanilla; beat until well mixed. Add flour; beat at low speed until well mixed.
Place dough into cookie press fitted with desired template. Press cookies, 2 inches apart, onto ungreased cookie sheets. Bake 5-8 minutes or until edges are set but not brown. Transfer to cooling racks; cool completely.
Melt 2 tablespoons butter in 1-quart heavy saucepan over medium heat. Cook 3-5 minutes, stirring constantly and watching closely, until butter just begins to turn golden brown. Immediately remove from heat. Cool slightly.
Combine browned butter and powdered sugar in bowl. Add 1 teaspoon vanilla and enough milk for desired glazing consistency. Drizzle over cooled cookies.
- If you don’t have a cookie press, place dough into piping bag with large open star tip; pipe 1- to 2-inch circles onto cookie sheet.
Video by Virtutrix