Heat oven to 375ºF. Line bottom of 15x10x1-inch baking pan with parchment paper; set aside.
Arrange clean thin cotton towel (about 34×20 inches) onto counter; sprinkle generously with unsweetened cocoa. Set aside.
Combine flour, 1/4 cup cocoa, baking powder and salt in bowl. Set aside.
Combine sugar, eggs and vanilla in another bowl; beat at high speed 5 minutes or until fluffy, thick and pale yellow color.
Stir melted butter into egg mixture; gently stir flour mixture into egg mixture until just combined. Spread into prepared pan.
Bake 10-12 minutes or until center springs back when touched. Run knife around edges to loosen sides.
Turn hot cake out onto prepared towel; remove parchment paper.
Cut cake in half lengthwise; lay short ends of cake onto prepared towel, touching end to end.
Cut 4 inches off one end; place next to one short end of cake. Beginning at same end, roll up cake in towel. Set aside to cool.
Beat 1/2 cup chilled whipping cream and 1/4 cup powdered sugar in chilled bowl; beat at medium-high speed, scraping bowl often, until stiff peaks form.
Place chocolate hazelnut spread and cream cheese in another bowl; beat at medium speed until well mixed.
Gently stir whipped cream mixture into chocolate mixture until just combined. Cover; refrigerate at least one hour.
Combine 1/3 cup butter and melted chocolate in bowl; beat at medium speed until well mixed.
Add 2 cups powdered sugar; beat at low speed until well mixed.
Add 3 tablespoons whipping cream; beat at medium-high speed until smooth and creamy.
Spread or dip bottom-side of meringue cookies into melted chocolate chips; attach marshmallow to bottom-side. Place onto waxed paper; let stand until set.
Dust tops of meringue cookies with cocoa, if desired.
Unroll cake; spread small cake with 1/4 cup chilled filling. Reroll; refrigerate until ready to assemble.
Spread large cake with remaining filling; reroll. Stand on end on serving plate. Frost sides.
Cut one end of small cake roll at angle. Place onto plate next to larger cake log so it angles out like a branch; secure with toothpicks or wooden skewers, as needed. Carefully frost sides of cake.
Draw lines in frosting, using fork for bark appearance, if desired.
Place meringue cookie mushrooms around yule log. Cover; refrigerate until serving.