Line a greased 15x10x1-in. baking pan with waxed paper. Grease the paper; set aside. In a large bowl, beat eggs for 3 minutes. Gradually add sugar; beat for 2 minutes or until mixture becomes thick and lemon-colored. Stir in zucchini and vanilla. Combine the flour, cocoa, baking soda, cinnamon and salt; add to egg mixture until well blended. (batter will be thick).
Spread batter evenly in prepared pan. Bake at 350° for 10-15 minutes or until cake springs back when lightly touched. Cool for 5 minutes. Invert onto a kitchen towel dusted with cocoa. Gently peel off waxed paper. Roll up cake in the towel jelly-roll style, starting with a short side. Cool completely on a wire rack.
For filling, in a large bowl, beat cream cheese, butter and vanilla until fluffy. Beat in confectioners' sugar until smooth.
Unroll cake; spread filling evenly over cake to within 1/2 in. of edges. Roll up again. Place seam side down on a serving platter. Dust with confectioners' sugar. Cover and refrigerate for 1 hour.