01 - Whisk together flour, baking powder, and salt in a medium bowl until well combined.
02 - Beat butter and granulated sugar in a large bowl until light and fluffy, approximately 2-3 minutes.
03 - Add egg and vanilla extract to the butter mixture, beating until fully incorporated.
04 - Gradually add flour mixture to the butter mixture, mixing until just combined. Be careful not to overmix.
05 - Divide dough in half, flatten into discs, wrap in plastic wrap, and refrigerate for at least 1 hour.
06 - Preheat oven to 350°F and line baking sheets with parchment paper.
07 - On a lightly floured surface, roll out dough to 1/4-inch thickness. Cut out rounds or shapes using a 2-inch cookie cutter.
08 - Place cookies 1 inch apart on prepared baking sheets. Bake for 8-10 minutes until edges just begin to turn golden. Cool completely on wire racks.
09 - Beat butter until creamy. Gradually add powdered sugar, then milk and vanilla extract. Beat until light and fluffy.
10 - Divide buttercream into small bowls and tint each with a different pastel food coloring, mixing until uniform color is achieved.
11 - Spread or pipe a layer of colored buttercream onto half of the cookies. Top with remaining cookies to form sandwiches.