Add the unsalted butter to a small saucepan over medium-low heat. Once melted, whisk in ¾ cup of the granulated sugar. Cook for 1–2 minutes, stirring frequently, until the mixture looks glossy and the sugar begins to soften. Do not let the mixture boil. Remove from the heat and allow it to cool slightly. It should remain warm, but not hot.

In a large mixing bowl, combine the whole egg, 2 egg yolks, and remaining ¾ cup granulated sugar. Using a hand mixer or stand mixer, beat on medium-high speed for 2–3 minutes, until the mixture becomes thick, pale, and creamy. Mix in the vanilla bean paste or vanilla extract.

Reduce the mixer speed to low. Slowly stream the warm butter and sugar mixture into the whipped eggs, mixing until fully incorporated and glossy. Scrape down the sides of the bowl as needed.

Sift the black cocoa powder, all-purpose flour, espresso powder, and fine sea salt directly into the bowl. Mix on low speed just until no dry streaks remain. Avoid overmixing.

Add the melted dark chocolate and gently fold until combined. Fold in the dark chocolate chips, chopped white chocolate, and white chocolate chips. Reserve a small handful of the chocolate pieces for topping, if desired.

Spread the brownie batter evenly into the prepared baking pan, smoothing the surface with an offset spatula. Sprinkle the reserved chocolate pieces over the top.

Bake for 35–42 minutes, or until the edges are set, the top is shiny and crackly, and the center still has a slight jiggle. A toothpick inserted into the center should come out with moist, fudgy crumbs rather than wet batter. Avoid overbaking.

Remove the brownies from the oven and immediately sprinkle with flaky sea salt.