Line a 9 × 11 in baking sheet with parchment paper. Preheat oven to 350 °F (175 °C).

In a large bowl, beat softened butter, granulated sugar, and brown sugar on medium speed until light and fluffy—about 2 minutes.

Mix in the whole egg until fully incorporated, then the egg yolk. Scrape the bowl and beat in vanilla.

In a separate bowl whisk together flour, matcha, cornstarch, baking soda, and salt.

With the mixer on low, add dry ingredients to the wet in two additions, mixing just until no flour streaks remain. Fold in white-chocolate chunks.

Scoop 1 ½-Tbsp mounds of dough 2 in apart on the prepared sheet.

For thicker cookies: refrigerate the scooped dough 20–30 minutes.

Bake 11–13 minutes, until edges are set and tops look slightly puffed but still soft. (They’ll finish setting on the sheet.) Immediately press a few extra white-chocolate pieces into the tops for a bakery look.

Let cookies rest on the sheet 5 minutes, then transfer to a wire rack to cool completely—or sneak one warm for maximum gooeyness!