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 incorporated.
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. To one portion, add the freeze-dried strawberry powder or food coloring and strawberry extract, mixing until evenly colored. To a second portion, add the cocoa powder and milk, mixing 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. Place 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 cookies to rest on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.