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.
Pour filling into 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.