Cream the softened butter and sugar together in a mixing bowl until the mixture is light, fluffy, and slightly pale, about 2-3 minutes, with a rhythmic whir and a smooth texture.
Add the egg and vanilla extract to the creamed mixture, whisking until well combined. The mixture should become slightly glossy and homogeneous.
In a separate bowl, whisk together the flour and baking powder. Gradually add this dry mixture to the wet ingredients, folding gently until just incorporated and a soft dough forms.
Divide the dough into two equal portions. In one, mix in the matcha powder until evenly colored, creating the green dough. In the other, gently fold in the strawberry purée for the pink dough. Wrap each in plastic wrap and chill in the fridge for about 30 minutes to firm up.
Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. Lightly dust a work surface with flour and roll out each dough portion into a rectangle about ¼ inch thick.
Place the pink and green rectangles side by side. Gently fold or layer them to create a layered effect, then press lightly to adhere.
Using a sharp knife or dough cutter, cut the layered dough into strips or slices about 1 inch wide. Twist or gently swirl these slices to enhance the marbled effect.
Arrange the twisted or layered dough pieces on the prepared baking sheet, spacing them about 2 inches apart. Bake in the preheated oven for 10-12 minutes, or until the edges are golden and fragrant.
Remove the cookies from the oven and let them cool on the baking sheet for a few minutes before transferring to a wire rack. The cookies will be crisp on the outside yet tender inside, with colorful swirls visible throughout.
Enjoy these vibrant, marbled cookies as a playful treat that combines visual appeal with a delightful crunch and tender crumb.