01 - In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
02 - In a large bowl, beat the softened butter and sugar with an electric mixer until light and fluffy, about 2 minutes.
03 - Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract until fully combined.
04 - Gradually add the dry ingredient mixture to the wet ingredients and mix until just combined. Do not overwork the dough.
05 - Split the dough into three equal portions. Knead the freeze-dried strawberry powder into one portion until evenly colored. Mix the cocoa powder and milk into a second portion until well blended. Leave the third portion plain for the vanilla layer.
06 - Place each dough portion on parchment paper or plastic wrap and shape into a flat rectangle approximately 8 × 4 inches. Stack the rectangles on top of one another — chocolate on the bottom, vanilla in the middle, and strawberry on top — gently pressing so the layers adhere.
07 - Wrap the layered dough tightly and refrigerate for at least 45 minutes until firm.
08 - Preheat the oven to 350°F. Line baking sheets with parchment paper.
09 - Using a sharp knife, slice the chilled dough crosswise into ¼-inch thick rounds. Place the cookies 1 inch apart on the prepared baking sheets.
10 - Bake for 10 to 12 minutes, until the edges are just beginning to turn golden.
11 - Allow the cookies to rest on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.