How to Make It
To prepare cake, preheat oven to 400°F. Lightly coat a 10- x 15-inch rimmed baking sheet with baking spray. Line bottom of pan with parchment paper. Coat paper with baking spray.
Microwave coffee and chocolate in a microwave-safe bowl at HIGH 30 to 45 seconds, stirring every 15 seconds, until smooth. Let stand 10 minutes.
Weigh or lightly spoon flour into a dry measuring cup; level with a knife. Whisk together flour, salt, and 1/4 cup cocoa in a small bowl. Beat egg yolks, 1/2 teaspoon vanilla, and 2 tablespoons granulated sugar in a large bowl with a mixer on medium-high speed until very thick and pale yellow, about 6 minutes. Gently fold coffee mixture into egg yolk mixture until almost combined but still streaky.
Using clean, dry beaters, beat egg whites and cream of tartar in a medium bowl with mixer on medium speed until foamy. Increase speed to high, and beat until soft peaks form, about 1 minute. Add remaining 1 tablespoon granulated sugar, and beat just until stiff peaks form, 1 to 2 minutes. (Do not overbeat.) Stir one-fourth of egg white mixture into yolk mixture; gently fold in remaining egg white mixture until almost combined but still streaky. Sift half of flour mixture over egg mixture; gently fold until dry ingredients are just moistened, and repeat with remaining half of flour mixture. Pour batter evenly into prepared pan, and gently spread to edges, taking care not to deflate batter.
Bake 8 minutes or until cake springs back when lightly touched in the center. Sprinkle a clean dish towel with remaining 2 tablespoons cocoa. Run an offset spatula or knife around sides of pan to loosen cake; immediately invert onto prepared towel. Starting at 1 short side, gently roll up parchment, warm cake, and towel together. Cool completely on wire rack, about 45 minutes.
To prepare filling, beat yogurt, cream, and 1 teaspoon vanilla with a mixer on medium speed until thickened, about 1 minute. Add powdered sugar; increase speed to medium-high, and beat until stiff peaks form, 1 to 2 minutes.
To assemble cake, gently unroll cake; peel off and discard parchment, and remove towel. (Cake may crack slightly as you unroll.) Spread filling over cake, leaving a 1-inch border around edges. Starting at short side, reroll cake; place, seam side down, on a platter. Cover and chill 30 minutes. Cut cake into 10 slices.