Melt the butter over low heat. Remove from the heat and let cool for a few minutes. Whisk in the sugar until smooth and glossy.

Whisk in the egg and egg yolk until fully incorporated.

Add the cocoa powder, salt, baking powder, and flour. Stir just until no dry streaks remain, then fold in the dark chocolate.

Spread half the batter evenly in the prepared pan. Arrange the white chocolate in a single layer over the batter, leaving a small border around the edges. Top with the remaining batter and smooth the surface.

Sprinkle lightly with flaky sea salt.

Bake until the top is set and crackly and the edges are just firm, 25 to 27 minutes. The center should still look slightly underdone. For an even gooier center, bake for about 20 minutes.

Transfer the pan to the freezer and chill until the brownies are firm enough to slice cleanly, 45 to 60 minutes.

Store in an airtight container in the refrigerator for up to 5 days.