Preheat oven to 350°F. Line a 9×13-inch pan with foil and spray the foil with nonstick cooking spray.
Place the chopped unsweetened baking chocolate and sliced unsalted butter in a large microwave-safe bowl. Heat on high in 30-second increments, stirring between each, until the chocolate and butter are melted and smooth (about 2 minutes, depending on your microwave).
Stir the granulated sugar and unsweetened cocoa powder into the melted chocolate and butter using a spatula or wooden spoon. Stir in the eggs and vanilla extract, then stir in the salt. The mixture will look grainy at first but should be smooth after mixing.
Stir in the all-purpose flour carefully until just combined. Pour the batter into the prepared pan and smooth the top.
Bake for 25-35 minutes, or until the top is no longer glossy and a toothpick inserted 2 inches from the side of the pan comes out with just a few crumbs. Cool completely in the pan before slicing. (The recipe author prefers 25 minutes for a very fudgy texture; bake longer if you want less fudgy brownies.)