Preheat the oven to 350°F.
Line an 8-inch square pan with aluminum foil.
Place bittersweet chocolate, unsweetened chocolate and butter in a large microwave-safe bowl. Microwave for 2-3 minutes, stirring every 30 seconds (don't skip this step or the chocolate will scorch!) until mixture is melted. Cool to lukewarm (don't skip this step either or the eggs will curdle!).
Once mixture is cooled, stir in the sugar, pinch of salt, and vanilla until combined.
Beat in the eggs by hand, one at a time.
Add the flour and stir energetically for 3-5 minutes until the batter is thick, smooth, and 'dry'. It will look curdled at first and may have some separated liquid, but if you stir it thoroughly it will reach the correct consistency. (This step is the most important to ensure the brownies have the perfect consistency!).
Scrape the batter into the prepared pan and bake until the center feels almost set (with a few dry crumbs when tested), about 20-30 minutes. Do not overbake!
Let the brownies cool completely in the pan before serving. (Note: These brownies will 'mature' and improve in flavor and texture the following day or two after baking. Don't eat them all the first day and you will see what I mean!).
These brownies can be stored, tightly covered with aluminum foil, at room temperature for up to a week.