Preheat your oven to 320°F (160°C) for fan-forced or 338°F (170°C) for conventional. Line two baking sheets with parchment paper.In a heatproof bowl set over a pan of gently simmering water (double boiler), combine the chopped dark chocolate and cubed butter. Stir occasionally until completely melted and smooth. Remove from heat, stir in vanilla, and let cool slightly.
In a separate large bowl, combine the room-temperature eggs, granulated sugar, and Demerara sugar. Using an electric mixer, beat on medium-high speed for 5-6 minutes until the mixture is very pale, thick, and has tripled in volume. When you lift the whisk, it should leave a thick ribbon that holds for a few seconds before dissolving.
In a small bowl, whisk together the flour, cocoa powder, baking powder, and salt.Pour the slightly cooled chocolate mixture into the whipped eggs. Gently fold with a spatula until about halfway combined. Add the dry ingredients and chocolate chips, then fold gently but firmly until just combined and no dry streaks remain. The batter will be thick and glossy.
Using a cookie scoop or tablespoon, drop mounds of dough (about 1.5 Tbsp each) onto the prepared sheets, spacing them at least 3 inches (7-8 cm) apart. Do not flatten.Bake for 12-14 minutes. The brookies are done when the tops are crackled, the edges look set, but the centers still appear soft. They will firm up as they cool.
Remove from the oven and immediately sprinkle with a pinch of flaky sea salt (if using). Let the brookies cool on the baking sheet for 10 full minutes before transferring them to a wire rack to cool completely. This sets their perfect fudgy-chewy texture.