The cookie recipe is "Old Fashioned Christmas Cookies" from the Southern Living Cookie Book. I couldn't find this old recipe anywhere online to link to, so I'm sharing it below!
Ingredients
1 cup butter, softened
2 cups sugar
¼ cup firmly packed brown sugar
2 eggs
6 tablespoons milk
2 teaspoons vanilla extract
4 cups all-purpose flour
2 teaspoons baking powder
½ teaspoon salt
Frosting
½ cup (1 stick) unsalted butter, softened
¼ teaspoon salt
2 teaspoons vanilla
⅓ cup milk
4 cups powdered sugar
Instructions
Make the cookies: Heat oven to 350°F. Line a baking sheet with parchment or a nonstick baking mat (Silpat).
In the bowl of an electric mixer, beat the butter on medium high speed until smooth and creamy, about 1 minute. Add the sugars to the butter and beat 2 minutes more or until light and fluffy. Add the eggs, one at a time, beating until just combined. Add the milk and vanilla and beat until just combined.
In a medium mixing bowl, combine the flour, baking powder and salt. Add the flour mixture to the butter mixture and beat until combined. Do not over mix. Wrap dough in plastic wrap and refrigerate at least 1 hour or up to 1 day.
Roll dough to ¼-inch thickness on floured surface. Cut into desired shapes and place cookies, 1 inch apart, on baking sheet. Bake 10 to 12 minutes or until just barely golden brown around the edges. Cool 5 minutes on baking sheet. Transfer to wire cooling rack and cool completely.
Meanwhile, prepare the frosting: In the bowl of an electric mixer, beat the butter and salt until smooth and creamy, about 1 minute. Add in the vanilla and milk and beat until just combined. Beat in the powdered sugar, 1 cup at a time, until frosting is smooth and creamy. Frost cookies with frosting.
Recipe by Espresso and Cream at https://www.espressoandcream.com/2016/12/cut-sugar-cookies-buttercream-frosting.html