Beat butter and granulated sugar with a stand mixer fitted with a paddle attachment on medium speed until light and fluffy, about 2 minutes. Add egg, vanilla, and (if using) almond extract. Beat until fully incorporated, about 30 seconds. Gradually add flour and salt, beating on low speed until combined, about 1 minute. Remove dough; shape into a flat disk about 1 inch thick. Wrap in plastic wrap; chill at least 2 hours or up to 24 hours.

Preheat oven to 350°F. Line 2 baking sheets with parchment paper. Transfer dough to a lightly floured work surface; roll to ⅛-inch thickness. Using a 3 ½-inch stocking-shaped cutter, cut out 36 cookies. Arrange 2 inches apart on baking sheets.

Bake in 2 batches in preheated oven until cookies are slightly golden around edges but pale in the center, 6 to 10 minutes per batch. Do not overbake. Cool on baking sheets 5 minutes. Transfer to a wire rack; cool completely, about 30 minutes.

Beat powdered sugar and 6 tablespoons milk with a stand mixer fitted with a whisk attachment on medium speed until combined and smooth, 1 minute, stopping to scrape down bowl as needed. Beat in remaining 1 tablespoon milk 1 teaspoon at a time until desired consistency is reached. Place sprinkle (or sanding sugar) colors on separate plates. Spoon icing into a piping bag or a ziplock plastic bag with 1 small corner snipped off.

Working with 1 cookie at a time, pipe an icing border, and then flood with icing. Using a wooden pick, spread icing to edges and corners. While icing is still wet, dip the lower portion of the stocking in 1 color of sprinkles; dip the upper portion in another color of sprinkles. Let stand until set, about 1 hour.