For filling:
1/2 lb fine-quality bittersweet chocolate (no more than 60% cacao if marked), coarsely chopped
3/4 stick stick (6 tablespoons) unsalted butter, cut into 1/2-inch cubes
2 large eggs, lightly beaten
1/3 cup heavy cream
1/4 cup granulated sugar
1/4 teaspoon salt
1 teaspoon pure vanilla extract
Special equipment:
8-inch (20-cm) round springform pan
Garnish:
Unsweetened cocoa powder for sprinkling
Make filling while crust cools:
Melt chocolate and butter in a 2-quart heavy saucepan over low heat, stirring until smooth, then remove from heat and cool 5 minutes.
Whisk together eggs, cream, sugar, salt, and vanilla in a bowl. Whisk chocolate mixture into egg mixture until combined well.
Assemble and bake tart:
Pour filling into cooled crust and rap pan once on counter to eliminate any air bubbles. Bake until filling 1 inch from edge is set and slightly puffed but center trembles slightly when pan is gently shaken, 20 to 25 minutes. (Center will continue to set as it cools.)
Cool tart completely in pan on a rack, about 2 hours. Chill, uncovered, until center is firm, about 4 hours. Remove side of pan and sprinkle with cocoa to serve.
Cooks' notes:
Tart can be chilled up to 3 days. Cover loosely after tart is completely chilled (covering before may cause condensation).
Crust, without filling, can be made 1 day ahead and kept, covered, at room temperature.