Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper or foil, leaving an overhang on each end.
In a large microwave-safe bowl combine the chocolate and butter. Microwave in 30-second bursts, stirring between each burst, until the mixture is melted and smooth. Let cool slightly.
In a large bowl, use an electric mixer to beat the eggs and sugar on high speed until light and thick, about 3 to 5 minutes. Beat in the vanilla extract. Stir in the cooled chocolate mixture with a rubber spatula. Add the flour and salt, folding gently until well combined. Pour the batter into the prepared baking pan.
Bake for about 20 minutes, or until the brownies are slightly puffed but still moist in the center. Transfer the pan to a wire rack and cool completely before cutting into squares. Brownies can be stored in an airtight container at room temperature for 2 days.