Grease and line the bottom of a 9x13 (23x33cm) cake pan with parchment or wax paper.
Dust a clean, lint free towel generously with powdered sugar. You can also use wax or parchment paper, but they will hold onto moisture as the cake cools and make it sticky.
In a small bowl, sift together flour, baking powder and salt. Set aside.
In a large bowl, beat eggs and sugar on medium high until quadruple in volume and the eggs are light in color. You should be able to make a ribbon pattern on the surface of the eggs with the beaters. Fold in the dry ingredients a little at a time gently to avoid knocking out all the air. Next, gently mix in the vanilla. Pour the batter into your prepared pan, leveling carefully.
Bake 8 - 10 minutes or until the top bounces back and cake slightly pulls away from pan. Center of cake should reach 190F - 210F (88 - 99C.)
Turn out on well sugared towel. Roll up gently from short end while cake is still warm. Allow to cool completely on rack, about 1 hour.
Filling
In a large bowl, blend peanut butter, softened butter, vanilla until smooth. Gradually add in the powdered sugar to avoid lumps.
Unroll the cooled cake, spread the peanut buttercream, leaving 1" (5cm) gap at the end free of icing. Top the buttercream with jelly. Gently roll back up cake. Wrap in plastic wrap or aluminum foil. Chill until firm, about 1 hour. Remove cake 20 minutes before serving. If desired, sprinkle top with powdered sugar shortly before serving.
Notes
Taste the peanut butter frosting as you gradually add the sugar and stop when you get the desired sweetness.Instead of making the peanut butter frosting, try just peanut butter!