1 pound semisweet chocolate, chopped
1 cup (2 sticks) unsalted butter
1/4 cup coffee liqueur
1 teaspoon vanilla extract
7 large eggs, room temperature
1 cup sugar
Preheat oven to 350°F. Butter 9-inch-diameter springform pan with 2 3/4-inch-high sides. Line bottom of pan with parchment paper. Stir chocolate, butter, coffee liqueur, and vanilla in heavy large saucepan over low heat until melted and smooth. Cool to lukewarm. Using electric mixer, beat eggs and 1 cup sugar in large bowl until thick and pale, and slowly dissolving ribbon forms when beaters are lifted, about 6 minutes. Fold 1/3 of egg mixture into lukewarm chocolate mixture. Fold remaining egg mixture into chocolate mixture.
Place prepared pan on baking sheet. Transfer batter to prepared pan. Bake until tester inserted into center comes out with moist crumbs attached, about 55 minutes. Cool 5 minutes. Gently press down edges of cake. Cool completely in pan. (Cake can be prepared up to 1 day ahead. Cover with plastic wrap and refrigerate. Let stand at room temperature 1 hour before continuing.)
Run knife around pan sides to loosen cake. Remove sides of pan; transfer cake to platter. Remove parchment paper. Sprinkle cake with powdered sugar and serve.