For the cake: Preheat the oven to 350˚. Butter a 12-by-17- inch rimmed baking sheet. Line with parchment paper, leaving an overhang on all sides. Butter the parchment.  Beat the egg whites, cream of tartar and salt in a large bowl with a mixer on medium-high speed until frothy. Add 1/4 cup granulated sugar and beat on high speed until stiff, glossy peaks form, about 2 minutes.  Sift together the flour, cocoa powder and baking powder in a medium bowl. In a separate large bowl, combine the egg yolks, the remaining 1/2 cup sugar and the vanilla. Beat on high speed until thick and creamy, 3 to 4 minutes. Beat in the melted butter and coffee until combined.  Add the flour mixture to the yolk mixture and beat on low speed until well combined. Fold a spoonful of the beaten egg whites into the batter until no streaks remain. Gently fold in the remaining egg whites until combined. Transfer the batter to the prepared pan, gently nudging the batter so it fills the corners. Give the pan a little shimmy to even it out. Bake until the top just starts to spring back when gently pressed, 10 to 12 minutes (the top might still feel a little tacky). Do not overbake or the cake will crack.  Place a clean dish towel on a large wire rack. Dust with 2 tablespoons powdered sugar. While the cake is still hot, loosen the edges from the pan, then turn out the cake onto the towel; carefully remove the parchment. Dust the top with the remaining 2 tablespoons powdered sugar.  Starting at one of the long sides, use the towel to tightly roll up the cake with the towel inside. Position the cake seam-side down and let cool about 1 hour.  For the filling: Beat the cream cheese in a large bowl with a mixer on low speed until just smooth. Add the powdered sugar and beat until smooth, about 1 minute. Gradually beat in the heavy cream 1/4 cup at a time, making sure the mixture is smooth before adding more cream. Increase the speed to medium high and beat until stiff peaks form, 2 to 4 minutes. Add the vanilla and beat for a few more seconds, just to combine. Carefully unroll the cooled cake and spread evenly with the filling, leaving a 1/4- to 1/2-inch border on all sides. Re-roll the cake, using the towel to help you. Cover the cake roll with parchment paper and then tightly wrap in plastic wrap. Chill for at least 2 hours.  Meanwhile, for the frosting: Put the chocolate in a medium bowl. Bring the heavy cream and corn syrup to a simmer in a saucepan, then pour over the chocolate. Let sit for 5 minutes, then whisk until smooth. Let thicken at room temperature until spreadable, about 2 hours.  Unwrap the cake on a cutting board. Cut off one-fourth of the cake on a sharp diagonal for the branch. Position the branch against the remaining cake roll on a platter. Cover the cake with the frosting using an offset spatula, then drag a fork through the frosting to create a bark-like texture. Garnish with rosemary sprigs and pomegranate seeds.