Preheat your oven to 175°C (350°F). Grease a 9-inch round or 8x8-inch square baking pan and line the bottom with parchment paper for easier removal.

Melt the butter and semi-sweet chocolate together in a heatproof bowl set over simmering water, or microwave in 20-second intervals, stirring each time, until smooth. Cool for 5 minutes.

In a large bowl, whisk together the sugar, brown sugar, eggs, and vanilla extract until smooth and slightly thickened.

Pour in the melted chocolate-butter mixture and whisk until fully combined.

In a separate bowl, sift together the flour, cocoa powder, baking powder, and salt.

Gently fold the dry ingredients into the wet ingredients using a spatula. Mix just until you see no streaks of flour; do not overmix.

Pour the batter into the prepared baking pan. Smooth the top with a spatula.

Bake for 28-32 minutes or until the top is set and a toothpick inserted in the center comes out with a few moist crumbs (not wet batter).

Remove from the oven and allow the brownie cake to cool in the pan for 15 minutes. Then transfer to a cooling rack to cool completely before slicing.