01 - Preheat oven to 350°F (175°C). Line two baking sheets with parchment paper.
02 - In a medium bowl, whisk together all-purpose flour, baking powder, and salt until well blended.
03 - In a large mixing bowl, beat the softened butter and granulated sugar with an electric mixer until pale and fluffy, 2–3 minutes.
04 - Beat in the egg and vanilla extract until fully incorporated.
05 - Gradually mix in the dry ingredients, scraping down sides as needed, until a soft cookie dough forms.
06 - Divide dough into two equal portions, wrap each in plastic wrap, and chill for at least 30 minutes to firm up.
07 - On a lightly floured surface, roll each portion of dough to 1/4-inch thickness. Cut cookies using a 2-inch round or festive-shaped cutter.
08 - Arrange cut cookies 1 inch apart on prepared baking sheets.
09 - Bake 10 to 12 minutes until edges are lightly golden. Cool on baking sheets for 5 minutes, then transfer to wire racks to cool completely.
10 - Beat the softened butter until creamy. Gradually add powdered sugar, vanilla, and 1 tablespoon milk, beating until smooth and fluffy. Add extra milk if needed for desired consistency.
11 - If desired, divide frosting and tint with food coloring. Spread or pipe about 1 tablespoon frosting onto the flat side of half the cookies. Top each with a remaining cookie to form sandwiches.
12 - Roll edges of assembled cookies in holiday sprinkles for festive decoration.