01 - In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
02 - In a large bowl, beat the softened butter and granulated sugar with an electric mixer until pale, light, and fluffy, approximately 2 minutes.
03 - Add the eggs one at a time, beating well after each addition. Mix in the pure vanilla extract until fully incorporated.
04 - Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed until the dough just comes together. Do not overmix.
05 - Split the dough into three equal portions. Add the freeze-dried strawberry powder (or food coloring and strawberry extract) to one portion and mix until evenly colored. Add the cocoa powder and milk to a second portion and blend thoroughly. Leave the third portion plain for the vanilla layer.
06 - Place each dough portion on a sheet of parchment paper or plastic wrap and shape into a flat rectangle approximately 8 x 4 inches.
07 - Layer the three rectangles on top of each other—chocolate on the bottom, vanilla in the center, and strawberry on top. Gently press together so they adhere. Wrap tightly and refrigerate for at least 45 minutes until very firm.
08 - Preheat the oven to 350°F. Line baking sheets with parchment paper.
09 - Using a sharp knife, slice the chilled dough log crosswise into ¼-inch thick rounds. Arrange the slices 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.