01 - Whisk together the flour, baking powder, and salt in a medium bowl until thoroughly blended. Set aside for later use.
02 - Beat the butter and granulated sugar on medium speed in a large mixing bowl until the mixture becomes light and fluffy, approximately 2 to 3 minutes.
03 - Add the egg and vanilla extract to the butter mixture, beating until completely incorporated and smooth.
04 - Gradually add the dry ingredient mixture to the wet ingredients, mixing just until the flour disappears. Avoid overmixing to prevent tough cookies.
05 - Divide the dough into two equal portions, flatten each into a disc shape, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes to firm.
06 - Preheat the 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 and arrange 1 inch apart on the prepared baking sheets.
08 - Bake for 8 to 10 minutes until the edges begin to turn slightly golden. Allow cookies to cool on the baking sheets for 2 minutes, then transfer to wire racks to cool completely.
09 - Beat the butter until creamy and smooth. Gradually add the powdered sugar, milk, vanilla extract, and salt, continuing to beat until the frosting becomes light and fluffy.
10 - Divide the prepared buttercream into several small bowls. Add a small amount of pastel gel food coloring to each bowl, mixing until the desired pastel shades are achieved.
11 - Spread or pipe a generous layer of colored buttercream onto the flat side of half the cooled cookies. Place remaining cookies on top, flat side down, to create sandwich cookies.
12 - Allow the assembled cookie sandwiches to set for 20 minutes at room temperature to allow the filling to firm slightly before serving.