Preparation

Make the cookies

• Sift the flour, baking soda, and salt into a large bowl.
• In a stand mixer fitted with the paddle attachment or in a large bowl using a hand mixer, beat the butter and sugar on medium speed until light and fluffy, about 2 minutes. Add the egg and vanilla, and beat to combine. In three additions each, alternately add the dry ingredients and sour cream, beating after each addition. Beat on medium speed until well combined, taking care to not overmix the dough, which will be sticky.
• Divide the dough into three portions and wrap each portion in plastic wrap. Refrigerate for at least 8 hours and up to 24 hours before using for the flavors to develop. (Or freeze for up to 1 month and thaw overnight in the refrigerator.)
• Position racks in the upper and lower thirds of the oven, and heat to 400°F. Line 2 or more baking sheets with parchment.
• Heavily flour a work surface and a rolling pin, then roll one piece of dough to between 1/8 and 1/4 inch thick. Working quickly so that the dough stays cold, cut out shapes using floured cookie cutters or a knife. Transfer to the baking sheets, spacing the cookies about 1 inch apart. Refrigerate for at least 30 minutes before baking. Repeat with the rest of the dough, rerolling scraps, if you have them, to make more cookies.
• Bake two sheets at a time, rotating and switching their positions halfway through, untilthe bottoms of the cookies are golden brown, 7 to 9 minutes. Transfer the cookies to a rack and cool completely before icing.

Make the icing

• Combine the confectioners’ sugar and salt in a large bowl. Melt the butter in a medium saucepan over low heat. Add the milk and bring to a boil over medium-high heat. Whisk in the sugar mixture, then the vanilla, and cool to room temperature. Add food coloring to batches of the icing, if you like, and then ice and decorate the cookies as you like. Store in a single layer for up to 2 days.