01 - Whisk together the flour, baking powder, and salt in a medium bowl until thoroughly combined.
02 - Beat the butter and granulated sugar on medium speed for 2–3 minutes until the mixture appears light and fluffy.
03 - Incorporate the egg and vanilla extract into the butter mixture, mixing until completely blended.
04 - Gradually add the dry ingredients to the wet mixture, mixing just until the flour disappears. Avoid overmixing.
05 - Divide the dough into two equal portions, flatten each into a disc, wrap tightly in plastic wrap, and refrigerate for 30 minutes.
06 - Preheat the oven to 350°F and line two baking sheets with parchment paper.
07 - Roll one dough disc on a lightly floured surface to ¼-inch thickness. Cut rounds using a 2-inch cookie cutter and arrange 1 inch apart on the prepared baking sheets.
08 - Bake for 8–10 minutes until the edges barely begin to turn golden. Allow to cool on the baking sheets for 2 minutes, then transfer to cooling racks.
09 - Beat the butter until creamy. Gradually add the powdered sugar, milk, vanilla, and salt, continuing to beat until the frosting achieves a smooth, fluffy consistency.
10 - Portion the buttercream into separate small bowls and tint each with a different pastel food coloring, mixing until the desired color is reached.
11 - Spread or pipe a generous layer of tinted buttercream onto the flat side of half the cooled cookies. Top with the remaining cookies to form sandwiches.
12 - Allow the assembled cookie sandwiches to rest for 20 minutes so the filling sets properly before serving.