Adjust oven rack to center position and heat oven to 350 degrees F. Lightly grease an 8- by 8-inch, 9- by 9-inch, or 9- by 13-inch baking pan. Line bottom and up two sides of pan with parchment paper (or foil), with ends of parchment paper extending over sides of pan to form handles. Grease parchment paper (or mist foil with cooking spray).

Bring water to a boil in bottom of double-boiler. Combine unsweetened chocolates, bittersweet chocolate and butter in top of double-boiler set over steaming water and melt gently while stirring. When mostly melted, remove from heat and continue stirring until mixture is completely melted and smooth. Set aside and let cool to lukewarm.

In a large bowl, or the bowl of a stand mixer, combine eggs and sugar, and beat until mixture is thick and very pale (at least 3-4 minutes if beating by hand or 1-2 minute if using electric beaters or a mixer). Beat in vanilla and set aside. In a small bowl sift together flour, cocoa powder and salt.

Pour warm chocolate into sugar and egg mixture and stir until well blended. Add flour mixture to the chocolate/egg mixture in three additions, gently folding after each addition until just incorporated. Scrape batter into prepared pan and spread evenly.

Bake for about 45 to 50 minutes for an 8- by 8-inch pan, 40 to 45 minutes for a 9- by 9-inch pan, or 35 to 40 minutes for a 9- by 13-inch pan. Check brownies for doneness several minutes before minimum baking time is reached. The surface should be shiny and may be cracking slightly. As soon as a toothpick inserted near the center comes out with a few fudgy crumbs still clinging to it instead of batter, they are done. Do not overbake. (It is better to underbake brownies than to overbake them.)

Remove from oven and let cool in pan set on wire rack. Using parchment paper (or foil) handles, carefully remove whole brownie cake from pan and cut into desired size and shape brownies. Store in tightly covered container at room temperature for gooey brownies, or in the refrigerator for denser brownies. Brownies may be frozen for up to 2 months.

Makes about 16 to 24 servings, depending on size of pan, and size and shape you cut brownies.