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