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Preheat the oven to 350 F. Line a 9- by 13-inch baking pan with parchment paper.
In a large bowl, whisk together the sugar, melted butter and vanilla.
Add the eggs one at a time, whisking until the egg is well incorporated after each addition.
Add the melted chocolate and whisk until smooth.
Using a spatula, stir in the flour, cocoa powder, salt and baking powder until combined.
Pour the batter into the prepared pan and smooth out the top with the spatula.
Bake for 40 to 50 minutes, until a cake tester inserted into the center comes out only slightly gooey.
Remove from the oven and let cool in the pan for at least 30 minutes at room temperature and then up to an hour in the fridge to make cutting into squares a breeze.
Store in an airtight container for 3 to 4 days, or in the freezer for up to a month.