Glazed Spiced Snowflake Cookies

Whisk together flour, baking soda, salt, and spices. In a large bowl, beat butter with brown sugar on medium-high speed until light and fluffy, about 3 minutes. Add half of flour mixture, then 1/3 cup water, then remaining flour mixture, beating on low after each addition until just incorporated. Shape dough into 3 disks and wrap in plastic. Refrigerate until firm, at least 1 hour and up to overnight.

Working with one disk at a time, roll out to 1/4 inch thick on lightly floured parchment. Cover with a doily; gently roll to make an imprint. (Dough should now be about 1/8 inch thick.) Remove doily and freeze dough until firm, about 15 minutes. Cut dough first using a 5-inch snowflake-shaped cutter, then cut remaining dough using a 3-inch snowflake-shaped cutter and 1 1/2-inch snowflake-shaped cutter. Chill and reroll scraps. Arrange large cookies on one parchment-lined baking sheet and medium and small cookies on another; freeze until firm, about 15 minutes. Preheat oven to 325 degrees.

Bake until cookies set around edges, 16 to 18 minutes for large, 12 to 14 minutes for medium and small. Transfer cookies on sheets to wire racks; let cool completely.

Whisk together confectioners' sugar, milk, and vanilla until smooth. If necessary, add more milk, 1/2 teaspoon at a time, until glaze is slightly thicker than heavy cream. Dip each cookie, design-side down, into glaze, tilting to evenly coat, then transfer to rack until glaze is set, about 10 minutes. Cookies can be stored in an airtight container at room temperature up to 3 days.