01 - Whisk together the flour, baking powder, and salt in a medium bowl. Set aside for later use.
02 - Beat the butter and sugar on medium speed until light and fluffy, approximately 2–3 minutes.
03 - Add the egg and vanilla extract, mixing until thoroughly combined.
04 - Gradually incorporate the dry ingredients, mixing just until the dough comes together.
05 - Divide dough in half, flatten into discs, wrap in plastic, and refrigerate for at least 30 minutes.
06 - Preheat oven to 350°F. Line two baking sheets with parchment paper.
07 - On a lightly floured surface, roll one disc to ¼ inch thickness. Cut rounds with a 2-inch cookie cutter, placing 1 inch apart on prepared sheets.
08 - Bake for 8–10 minutes until edges just begin to turn golden. Cool on sheets for 2 minutes, then transfer to racks to cool completely.
09 - Beat butter until creamy. Gradually add powdered sugar, milk, vanilla, and salt, beating until smooth and fluffy.
10 - Divide buttercream into small bowls and tint each with a different pastel food coloring.
11 - Spread or pipe a generous layer of buttercream onto the flat side of half the cookies. Top with remaining cookies to form sandwiches.
12 - Allow assembled cookies to set for 20 minutes before serving.