Line a 15x10x1-in. baking pan with waxed paper and grease the paper; set aside. In a large bowl, beat eggs for 5 minutes on medium speed or until lemon-colored. Gradually add the sugar, persimmon pulp and lemon juice; beat for 3 minutes. Combine the flour, cinnamon, baking powder, ginger, salt and nutmeg; add to egg mixture and beat well.
Spread batter evenly in prepared pan; sprinkle with pecans. Bake at 375° for 15 minutes or until lightly browned.
Cool in pan for 5 minutes. Turn cake onto a kitchen towel dusted with confectioners’ sugar. 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 small bowl, beat cream cheese and butter until smooth. Beat in the confectioners' sugar and vanilla until desired spreading consistency is reached.
Unroll cake and spread filling evenly over cake to within 1/2 in. of edges. Roll up again. Cover and refrigerate until serving. Dust with additional confectioners' sugar. Refrigerate or freeze leftovers.
As a substitute for 1 cup of self-rising flour, place 1-1/2 teaspoons baking powder and 1/2 teaspoon salt in a measuring cup. Add all-purpose flour to measure 1 cup.