Instructions

1. Arrange a rack in the middle of the oven and heat to 350°F.
2. Brush 1 tablespoon of the unsalted butter on the bottom and sides of a 9-inch springform pan. Sprinkle with 1 tablespoon of the cocoa powder. Holding the pan over the sink, move it in a circular motion to distribute the cocoa evenly over the buttered surfaces, discarding any excess into the sink; set aside.
3. Place the remaining 10 tablespoons butter and 10 1/2 ounces bittersweet or semisweet chopped chocolate in a large microwave-safe bowl. Microwave on the high setting in 15-second bursts, stirring between each burst, until the butter and chocolate are completely melted, 45 to 60 seconds total. Set aside to cool until the chocolate is warm, but not hot, 2 to 3 minutes.
4. Whisk 6 large egg yolks into the cooled chocolate mixture. Sift in the remaining 2/3 cup cocoa powder, 1/2 teaspoon espresso powder, and 1/4 teaspoon salt. Add 1 teaspoon vanilla extract and whisk until completely combined.
5. Place 5 large egg whites in the bowl of a stand mixer fitted with the whisk attachment. (Alternatively, use an electric hand mixer and large bowl.) Beat on low to medium speed until the egg whites are broken up and foamy, 15 to 20 seconds.
6. Add 1/2 teaspoon cream of tartar and beat on medium to medium-high speed until the whites form fluffy, droopy peaks when the beater is lifted, 45 to 90 seconds.
7. With the mixer on medium speed, gradually add 1 cup granulated sugar and beat until you've created glossy, stiff peaks that stand by themselves when you lift the beaters slightly, 1 to 2 minutes. The exact timing will depend on the size and shape of the bowl, the power of your mixer, and other factors.
8. Whisk about a 1/4 of the whipped egg whites into the chocolate mixture. Then, with a silicone spatula, gently scoop the remaining egg whites into the batter. With the same spatula, scoop them from underneath, along with some of the batter, and very gently turn the whole thing over; repeat until just incorporated on no streaks of egg whites remain.
9. Pour the batter into the prepared pan and smooth the top with a silicone spatula. Bake until the cake has risen ever-so-slightly in the center and is set enough in the center that it will not jiggle when the pan moves; a cake tester will not come out clean, 34 to 37 minutes. The top will have formed an extremely thin, but discernible, crust. The cake will pull away from the side of the pan while it cools; don't let it bake until it pulls away from the side of the pan while in the oven or it will be overdone. Cool completely on a wire rack for at least 1 1/2 hours. Remove the side of the pan and serve with melted chocolate and ice cream if desired.