Adjust an oven rack to the middle position; preheat oven to 325 degrees. Spray a 13x9-inch baking pan with nonstick spray. Line baking pan with parchment paper or foil and spray with nonstick spray again.

In a medium bowl, whisk the flour, salt, and baking powder together until combined. Set aside.

Melt the chocolate and butter in a large heatproof bowl over a saucepan of almost-simmering water, stirring occasionally, until smooth. Alternatively, in a microwave, heat the butter and chocolate in a microwave-safe bowl on high for 45 seconds, then stir and heat for 30 seconds more. Stir again, and, if necessary, repeat in 15-second increments until melted. When the chocolate mixture is completely smooth, remove the bowl from the saucepan and gradually whisk in the sugar. Add the eggs, on at a time, whisking after each addition until combined. Whisk in the vanilla. Add the flour mixture in 3 additions, folding with a rubber spatula until the batter is smooth.

Transfer the batter to the prepared pan; using a spatula, spread the batter into the corners of the pan and smooth the surface. Bake until a toothpick or cake tester inserted into the center of the brownies comes out with a few moist crumbs attached, 30-35 minutes. Cool on a wire rack to room temperature, then remove the brownies from the pan. Cut into 2-inch squares and serve. Brownies can be stored in an airtight container at room temperature for up to 3 days.