01 - Preheat the oven to 425°F. Generously butter four 6-oz ramekins and dust with flour, tapping out any excess.
02 - Sift together the matcha powder, flour, and salt in a small bowl until thoroughly blended.
03 - Place butter and white chocolate in a heatproof bowl set over a saucepan of simmering water. Stir constantly until completely melted and smooth, then remove from heat and let cool slightly.
04 - In a separate bowl, whisk together eggs, egg yolks, and sugar until thick, pale, and slightly foamy, approximately 2 minutes.
05 - Pour the melted chocolate mixture and vanilla extract into the egg mixture. Stir gently until fully incorporated.
06 - Gently fold the dry ingredients into the wet mixture, mixing just until no streaks remain. Be careful not to overmix.
07 - Divide the batter evenly among the four prepared ramekins, filling each about three-quarters full.
08 - Place ramekins on a baking sheet and bake for 11-13 minutes, until edges are set but centers remain soft and slightly jiggly.
09 - Let cool for 1 minute, then run a knife around the edges to loosen. Invert each cake onto a serving plate, dust with powdered sugar, and serve immediately with fresh berries if desired.