Preheat the oven to 350 degrees F. Line a 9-by-13-inch baking dish with aluminum foil, leaving about a 2-inch overhang of foil on at least 2 sides, and lightly coat with cooking spray.
Whisk the flour, baking powder and salt together in a medium bowl and set aside. Bring 1-inch of water to a simmer in medium saucepan over medium heat. Put both the semisweet and unsweetened chocolates and butter in a medium heatproof bowl that sits comfortably over the saucepan without touching the water. Stir occasionally until the chocolate melts and the mixture is smooth. Remove from the heat.
Whisk the sugar, vanilla and eggs together in a large bowl. Add the chocolate mixture and stir until blended and then stir in the flour mixture until just combined. Spread in the prepared baking dish.
Bake until a toothpick inserted into the center comes out with a few moist crumbs, 25 to 30 minutes. Cool the brownies completely in the pan on a wire rack. Lift the brownies out of the pan using the foil and cut into squares.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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