Preheat the oven to 350°F. Line a jelly roll pan with parchment paper, leaving some overhang on the long sides for easy lifting.
In a medium bowl, whisk together the flour, cocoa powder, baking powder, and salt until well combined.
In a large bowl, beat the eggs and granulated sugar with a mixer on high speed for 4 to 5 minutes, until thick, pale, and ribbony.
Add the vegetable oil, milk, and 1/2 teaspoon of the vanilla bean paste to the egg mixture and mix on low just until combined.
Gently fold the dry ingredients into the egg mixture with a spatula until the batter is smooth and no dry streaks remain.
Pour the batter into the prepared pan and spread it into an even layer, all the way to the corners.
Bake for 10 to 12 minutes, until the cake springs back lightly when touched in the center.
While the cake bakes, lay a clean kitchen towel on the counter and dust it generously with powdered sugar.
As soon as the cake comes out of the oven, run a knife around the edges, then invert the cake onto the prepared towel and carefully peel off the parchment paper.
Starting from a short side, roll the warm cake up with the towel inside. Place the rolled cake seam side down on a rack and let it cool completely.
For the filling, beat the peanut butter and powdered sugar in a bowl until smooth and thick.
Add the 1/2 cup heavy cream and the remaining 1/2 teaspoon vanilla bean paste to the peanut butter mixture and beat until light, fluffy, and spreadable.
Fold in the chopped peanut butter cups until evenly distributed.
Once the cake is completely cool, gently unroll it. Spread the peanut butter cup filling evenly over the surface, all the way to the edges.
Re-roll the cake without the towel, starting from the same short end, and place it seam side down on a serving platter or tray.
For the ganache, place the chocolate chips in a heatproof bowl. Heat the remaining 1/2 cup heavy cream in a small saucepan or microwave until steaming with small bubbles at the edges.
Pour the hot cream over the chocolate chips and let stand for 2 minutes, then stir slowly from the center out until smooth and glossy.
Let the ganache cool for a few minutes until slightly thickened, then spread or drizzle it over the cake roll, covering the top and sides as desired.
Chill the cake roll for 30 minutes, or until the filling is firm and the ganache is set to a soft, sliceable finish.
Slice with a sharp knife, wiping the blade between cuts for clean spirals. Garnish with extra chopped peanut butter cups if desired and serve chilled or slightly cool.