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 together using 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, mixing until just combined. Do not overmix.
05 - Divide the dough into three equal portions. Add the freeze-dried strawberry powder (or food coloring and extract) to one portion and mix until evenly colored. Add the cocoa powder and milk to a second portion and mix 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 x 4 inches.
07 - Layer the rectangles on top of each other—chocolate on the bottom, vanilla in the middle, and strawberry on top. Gently press together so the layers adhere. Wrap 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 log crosswise into ¼-inch thick slices. Arrange 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.