Coat a 15 x 10-inch jelly-roll pan with cooking spray; line bottom with wax paper. Coat wax paper with cooking spray. Dust with breadcrumbs; set aside.
Beat egg yolks in a bowl at high speed of a mixer for 4 minutes. Gradually add 1/4 cup sugar, beating until thick and pale (about 2 minutes). Beat egg whites with clean beaters at high speed of a mixer until foamy; add salt. Gradually add 1/2 cup sugar, 1 tablespoon at a time, beating until stiff peaks form. Stir in vanilla. Gradually add cocoa; stir until well-blended. Gently stir one-fourth of egg white mixture into egg yolk mixture; gently fold in remaining egg white mixture.
Spoon batter into prepared pan, spreading evenly to sides of pan. Bake at 375° for 15 minutes or until cake springs back when touched lightly in center. Loosen cake from sides of pan; turn out onto a dishtowel dusted with powdered sugar; carefully peel off wax paper. Let cake cool 1 minute. Starting at narrow end, roll up cake and towel together. Place, seam side down, on a wire rack; let cool completely (about 1 hour).
Unroll cake carefully; remove towel. Spread whipped topping over cake, leaving a 1/2-inch margin around outside edges. Reroll cake; place, seam side down, on a platter. Cover and chill 1 hour. Cut cake into slices. Drizzle syrup on each of 10 plates. Place cake slice on top; serve with raspberries.