01 - Whisk together flour, baking powder, and salt in a medium bowl until thoroughly combined. Set aside for later use.
02 - Beat butter and granulated sugar on medium speed in a large mixing bowl until light and fluffy, approximately 2 to 3 minutes.
03 - Add egg and vanilla extract to the butter mixture, mixing until fully incorporated and smooth.
04 - Gradually add dry ingredients to the wet mixture, mixing just until the flour disappears. Do not overmix.
05 - Divide dough in half and flatten into discs. Wrap tightly in plastic wrap and refrigerate for at least 30 minutes.
06 - Preheat oven to 350°F. Line two baking sheets with parchment paper and set aside.
07 - On a lightly floured surface, roll one dough disc to ¼ inch thickness. Cut rounds using a 2-inch cookie cutter. Arrange 1 inch apart on prepared baking sheets.
08 - Bake for 8 to 10 minutes until edges are just beginning to turn golden. Cool on sheets for 2 minutes, then transfer to cooling racks.
09 - Beat butter until creamy. Gradually add powdered sugar, milk, vanilla, and salt, beating until smooth and fluffy.
10 - Divide buttercream into small bowls. Add a small amount of pastel gel food coloring to each bowl, mixing until desired pastel shade is achieved.
11 - Spread or pipe a generous layer of buttercream onto the flat side of half the cooled cookies. Top with remaining cookies, pressing gently to adhere.
12 - Allow assembled sandwich cookies to set for 20 minutes at room temperature before serving.