Preheat oven to 375F. Line 15x10x1-inch baking pan with foil, with ends of foil extending over sides of pan. Grease foil; set aside.
Mix cookie crumbs, sugar, flour, baking powder and salt; set aside.
Mix water, melted chocolate and vanilla; set aside. Beat egg yolks in large bowl with electric mixer on high speed 5 min. or until thick and lemon colored. Gradually add flour mixture alternately with the chocolate mixture, beating until well blended after each addition. Beat egg whites with electric mixer on high speed until stiff peaks form; gently stir into batter.
Spread into prepared pan.
Bake 10 to 12 min. or until toothpick inserted in center comes out clean. Lift cake from pan, using foil handles. Invert cake onto clean cloth towel sprinkled with cocoa; remove foil.
Cut cake crosswise into thirds; place 2 of the cake pieces on wire racks to cool.
Roll up the remaining cake piece along with the towel, starting at one of the short ends of cake; cool completely.
Unroll cake and remove towel; spread cake with 1 cup of the ice cream. Re-roll cake; place, seam side down, in center of serving plate.
Spread 1 cup of the remaining ice cream onto each of the remaining 2 cake pieces. Wrap 1 of the pieces around the cake roll on the serving plate, with the ice cream layer facing the center cake roll. Repeat with the remaining cake roll, wrapping it around the other side of the center cake roll. Frost side of cake with 1 cup of the whipped topping. Freeze 4 hours or until firm.
Remove cake from freezer about 5 minutes before serving to soften slightly. Top with the remaining 1/2 cup whipped topping and strawberries just before serving. Store leftover dessert in freezer.
