Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper and set aside.
In a large mixing bowl, combine softened butter and granulated sugar. Use a hand or stand mixer to beat until the mixture is light and fluffy, about 2-3 minutes. Observe the pale, creamy color and increased volume.
Add the egg to the butter and sugar mixture. Mix until fully incorporated, with the mixture appearing smooth and slightly glossy.
In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add these dry ingredients to the wet mixture, mixing on low speed until just combined. The dough should come together and be slightly sticky but firm enough to handle.
Divide the dough into two equal portions. Mix the matcha powder into one portion until fully blended, and gently fold the berry puree into the other portion, creating a marbled effect. Use a silicone spatula to swirl the two halves together lightly, creating streaks of pink and green throughout the dough.
Scoop spoonfuls of the marbled dough onto the prepared baking sheet, spacing them about 2 inches apart. Slightly flatten each mound with the back of a spoon.
Bake in the preheated oven for 12-15 minutes, until the edges are golden brown and the cookies look set. The tops should still look slightly soft but hold their shape.
Remove the baking sheet from the oven and transfer the cookies to a cooling rack. Allow them to cool completely before handling to prevent breaking.
