Preheat your oven to 350°F (175°C). Grease a 10×15-inch jelly roll pan and line it with parchment paper, leaving some overhang on the sides for easy removal.

In a medium bowl, whisk together the flour, cocoa powder, baking powder, and salt. Set aside.

In a large mixing bowl, beat the eggs and granulated sugar together until light and fluffy, about 5-7 minutes. The mixture should be pale and thick. Stir in the vanilla extract.

Gradually add the dry ingredients to the egg mixture, mixing until just combined. Add the vegetable oil and whole milk, and gently fold the mixture until smooth.

Pour the batter into the prepared jelly roll pan and spread it evenly with a spatula.

Bake in the preheated oven for 10-12 minutes, or until the cake springs back when lightly touched and a toothpick inserted into the center comes out clean.

While the cake is baking, lay a clean kitchen towel on a flat surface and dust it generously with powdered sugar

Once the cake is done baking, carefully lift it out of the pan using the parchment paper overhang and place it on the powdered sugar-dusted towel. Remove the parchment paper.

Starting from one short end, gently roll the cake up with the towel, creating a spiral. Allow the cake to cool completely in the rolled position.

In a large mixing bowl, beat the heavy cream, powdered sugar, and vanilla extract together until stiff peaks form.

Once the cake has cooled, carefully unroll it. Spread the whipped cream filling evenly over the cake, leaving a small border around the edges.

Gently roll the cake back up, without the towel, and place it seam-side down on a serving plate.

In a heatproof bowl, place the finely chopped semi-sweet chocolate.

In a small saucepan, heat the heavy cream over medium heat until it just begins to simmer. Pour the hot cream over the chocolate and let it sit for a minute to melt.

Stir the mixture until smooth and glossy. Let the ganache cool slightly before pouring it over the Swiss roll.