Preheat your oven to 180°C (350°F). Prepare a 15x10 inch jelly roll pan by lining it with parchment paper, ensuring to lightly grease the surface of the paper.
In a large mixing bowl, whisk together the eggs and granulated sugar until the mixture becomes pale and fluffy, which should take about 5-7 minutes.
In a separate bowl, sift together the all-purpose flour, cocoa powder, baking powder, and salt. Gradually fold this dry mixture into the egg and sugar mixture, being careful not to overmix; stop when just combined.
Drizzle in the vegetable oil and gently fold it into the batter, ensuring it's well incorporated without deflating the mixture.
Pour the batter into the prepared jelly roll pan, spreading it out evenly with a spatula. Bake in the preheated oven for 12-15 minutes, or until the sponge bounces back when pressed lightly on top.
While the cake bakes, prepare a clean kitchen towel by dusting it with powdered sugar to prevent sticking.
Once the cake is finished baking, promptly remove it from the oven and invert it onto the prepared towel. Carefully peel away the parchment paper while the sponge is still warm.
Starting from one short end, roll the sponge tightly with the towel, then allow it to cool completely in this rolled position.
In a separate bowl, whip the heavy cream and powdered sugar together until soft peaks form, which indicates that it's ready for spreading.
After the sponge has cooled, gently unroll it and spread the whipped cream evenly across the surface. Layer the sliced strawberries on top of the cream.
Carefully roll the sponge back up without the towel, maintaining gentle pressure to keep it tight and ensure a nice shape.
Transfer the rolled cake to a decorative serving platter. Drizzle the melted dark chocolate generously over the top for an elegant finish.
Chill the Swiss roll in the refrigerator for at least 30 minutes to set everything before slicing and serving.
Notes
Serve with additional fresh strawberries and a dusting of powdered sugar for an elegant presentation.