Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium mixing bowl, whisk together the all-purpose flour, matcha powder, baking powder, baking soda, and salt. Set aside.
In a separate bowl, cream the softened butter, granulated sugar, and brown sugar using a hand mixer or a stand mixer fitted with a paddle attachment. Beat on medium speed until the mixture becomes light and airy. Add in the vanilla extract and the egg, mixing until fully incorporated. Scrape down the sides of the bowl as needed.
Gradually add the dry ingredients to the wet mixture, blending on low speed until a soft, cohesive dough forms. Be cautious not to overmix. Gently fold in the ruby and white chocolate chunks, reserving some to press on top of the cookies before baking.
Scoop out 2-tablespoon portions of dough, rolling them into balls. Place them on the prepared baking sheet, ensuring at least 2 inches of space between each one. Lightly press the reserved chocolate chunks onto the tops of the dough balls.
Transfer the baking sheet to the center rack of the oven and bake for 10 to 12 minutes, or until the edges turn lightly golden while the centers remain soft and slightly puffed.
As soon as the cookies come out of the oven, carefully tap the baking sheet against the counter a few times to create beautifully crinkled edges. Sprinkle each cookie with a pinch of flaky sea salt. Allow them to cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely.