Preheat oven to 375 degrees F. Grease and lightly flour a 15x10x1-inch jelly-roll pan. Stir together flour, baking powder, and salt in a small bowl. Set aside.
Beat egg yolks and vanilla in a medium mixing bowl with an electric mixer on high speed about 5 minutes or until thick and lemon-color. Gradually add the 1/3 cup sugar, beating on medium speed until sugar is almost dissolved. Fold in melted butter. Wash beaters.
Beat egg whites and cream of tartar in a large mixing bowl on medium to high speed until soft peaks form (tips curl). Gradually add the 1/2 cup sugar, beating until stiff peaks form (tips stand straight). Fold yolk mixture into whites mixture. Sprinkle flour mixture over egg mixture; fold in gently, just till combined. Spread evenly in prepared pan. Sprinkle with nuts.
Bake in the preheated oven for 12 to 15 minutes or until top springs back when lightly touched. Immediately loosen edges of cake; turn out onto towel sprinkled with powdered sugar. Starting with a narrow end, roll up cake and towel together. Cool on wire rack. Unroll cake. Spread jam evenly over cake to within 1 inch of edge. For the cannoli filling in a bowl stir together ricotta cheese, granulated sugar, and vanilla. Stir in bittersweet or semisweet chocolate shavings. Carefully spread Cannoli Filling evenly over jam layer to within 1 inch cake edges. Reroll cake. Cover and chill up to 2 hours.
To serve, cut cake on the bias into slices with a serrated knife. Transfer slices to individual dessert plates. If desired, sprinkle with chocolate shavings. Makes 10 servings.
Stir together ricotta cheese, sugar, and vanilla. Stir in bittersweet or semisweet chocolate shavings.