MOCHA FROSTING: Combine all the ingredients together in a bowl and then slowly add milk, (adding more if necessary). Mix until well blended to a smooth consistency. Refrigerate til needed.
CHEESECAKE FILLING: Place chocolate chips in small microwave-safe bowl. Microwave 30 seconds; stir. If necessary, microwave at an additional 15 seconds at a time, stirring after each heating, just until chips are melted when stirred. Set aside.
Beat cream cheese, sugar and butter in large bowl on medium speed of mixer until creamy. Gradually add melted chips, beating on low speed until blended. Fold in whipped topping until blended. Refrigerate until needed.
CAKE: Preheat oven to 350°F Line the bottom of a rimmed cookie sheet with parchment paper.
In small bowl, combine flour, cocoa, baking powder and salt. Set aside.
In large bowl, beat eggs, sugar, and vanilla until thick and creamy, about 4 minutes. Beat in flour mixture and melted butter. Spread in prepared pan and bake 10-14 minutes or until done.
Sprinkle a clean kitchen towel generously with confectioners sugar. Immediately invert cake onto towel. Gently peel off parchment paper. Roll warm cake from the long end with towel inside. Place seam side down on wire rack to cool.
Unroll cake. Stir cheesecake filling and spread onto cake within 1/2 of edges. Roll back up using the towel to help guide a good seal (like making sushi with a bamboo sheet). Cover with plastic wrap. Refrigerate for one hour, seam side down.
ASSEMBLY: Cut of 1/4 of each end. Cut off 1/3 of an end of the cake on the diagonal. Place the longer piece onto the platter you will be serving on. Place the short end on the side of the long piece to resemble a log with a thick branch sticking out.
Stir frosting to get it creamy again as this will make it easier to frost the cake. Spread frosting all over the cake with frosting except the ends. Using the tines of a fork, create the bark of the tree. Keep cake refrigerated.