Step 1: Preheat your oven to 375°F (190°C). Grease a 15x10-inch jelly roll pan and line it with parchment paper, leaving an overhang on the sides. Grease the parchment paper as well.
Step 2: In a medium bowl, whisk together the flour, baking powder, salt, and cocoa powder. Set aside.
Step 3: In a large bowl, beat the egg yolks with 3/4 cup of the granulated sugar until light and fluffy. Stir in 1 teaspoon of vanilla extract.
Step 4: In a separate clean bowl, beat the egg whites until soft peaks form. Gradually add the remaining 1/2 cup of granulated sugar and continue beating until stiff, glossy peaks form.
Step 5: Gently fold the flour mixture into the egg yolk mixture until just combined. Then, carefully fold in the stiff egg whites in two additions until no streaks remain, being careful not to deflate the batter.
Step 6: Pour the batter evenly into the prepared jelly roll pan and spread it to the edges. Bake for 12-15 minutes, or until the cake springs back when lightly touched.
Step 7: While the cake bakes, lay a clean kitchen towel on your counter and dust it generously with powdered sugar.
Step 8: As soon as the cake comes out of the oven, immediately invert it onto the prepared sugar-dusted towel. Carefully peel off the parchment paper.
Step 9: Starting from a short end, carefully roll up the warm cake and the towel together. Place the rolled cake seam-side down on a wire rack and let it cool completely, about 1-2 hours.
Step 10: While the cake cools, prepare the peanut butter frosting. In a large bowl, beat the softened butter and creamy peanut butter together until smooth. Gradually add the powdered sugar, alternating with milk/cream, until you reach a smooth, spreadable consistency. Beat in 1 teaspoon of vanilla extract.
Step 11: Once the cake is completely cool, carefully unroll it. Spread the peanut butter frosting evenly over the entire surface of the cake, leaving a small border around the edges. Sprinkle the chopped Reese's Peanut Butter Cups over the frosting.
Step 12: Carefully re-roll the cake, without the towel this time, starting from the same short end. Place the roll cake seam-side down on a serving platter. Cover loosely with plastic wrap and refrigerate for at least 30 minutes to allow the frosting to set.
Step 13: Before serving, garnish with additional chopped Reese's Peanut Butter Cups, if desired. Slice with a sharp knife and enjoy!