Melt white chocolate as directed on package; spread into 11x8-inch rectangle on parchment-covered baking sheet. Melt 1 oz. semi-sweet chocolate as directed on package. Drop in small spoonfuls over white chocolate; swirl gently with knife. Refrigerate until ready to use.
Spray 15x10x1-inch pan with cooking spray. Line with parchment; spray with additional cooking spray. Combine flour, baking powder and 1/4 cup cocoa powder. Beat egg whites in medium bowl with hand-held mixer on high speed until foamy. Gradually add 1/3 cup granulated sugar, beating constantly until stiff peaks form.
Beat egg yolks in large bowl with mixer on high speed until blended. Gradually add remaining granulated sugar, beating until thick and lemon colored. Blend in vanilla. Add flour mixture; mix well. (Mixture will be thick.) Add 1/3 of the beaten egg whites; stir gently just until blended. Gently stir in remaining egg whites. Spread onto bottom of prepared pan.
Bake 8 to 10 min. or until top of cake springs back when touched in center. Carefully run knife around edges to loosen cake. Sprinkle clean kitchen towel evenly with 2 Tbsp. of the remaining cocoa powder. (For best results, do not use a terrycloth towel.) Invert cake onto prepared towel; carefully peel off paper. Starting at one short side, roll up cake and towel together; place on wire rack. Cool completely. Meanwhile, melt remaining semi-sweet chocolate; cool slightly.
Mix cream cheese and powdered sugar in medium bowl until blended. Add melted chocolate; mix well. Stir in 3 Tbsp. coffee. Gently stir in COOL WHIP. Unroll cake; remove towel. Brush cake with remaining coffee. Reserve 1 cup cream cheese mixture for later use; spread remaining cream cheese mixture onto cake. Reroll cake.
Place filled cake, seam side down, on platter. Cut 2-inch-thick diagonal slice off one end of cake roll; place on top of cake as shown in photo, securing to cake roll with some of the reserved cream cheese mixture. Frost cake with remaining cream cheese mixture, leaving cut cake slice unfrosted as shown in photo. Cut white chocolate sheet into 3x1-1/2-inch pieces. Insert into cream cheese frosting on cake as shown in photo. Use kitchen shears to trim marshmallows to resemble mushrooms as pictured; sprinkle with remaining cocoa powder. Use to garnish cake.