Preheat your oven to 350°F (175°C). Line a 15×10-inch jelly roll pan with parchment paper and lightly grease the paper.

In a large mixing bowl, beat the eggs and granulated sugar on medium speed until the mixture becomes light and fluffy, about 5-7 minutes. Add the vanilla extract and combine.

In a separate bowl, whisk together the flour, baking powder, and salt. Gradually fold these dry ingredients into the egg mixture until just combined.

Pour the batter into the prepared pan, spreading it evenly. Bake for 10–12 minutes or until golden brown.

Remove the cake from the oven, let it cool slightly for 5 minutes. Turn the cake onto a kitchen towel dusted with powdered sugar, peel off the parchment, and roll the cake using the towel. Set aside to cool completely.

For the custard, heat the milk, heavy cream, and sugar over medium heat until steaming.

In a separate bowl, whisk together the egg yolks, cornstarch, and remaining vanilla until smooth. Gradually add the hot milk mixture to the egg yolks, whisking constantly.

Return everything to the saucepan and cook over medium heat, whisking until thickened, approximately 3-5 minutes. Stir in the butter until completely melted and smooth, then let it cool to room temperature.

Heat the heavy cream in a saucepan until it begins to simmer. Pour over the chopped chocolate and let it sit. Stir until smooth and mix in any remaining butter until glossy.

Gently unroll the cooled cake, spread the custard evenly over the surface, then roll it back up seam-side down on a serving platter.

Pour the ganache over the top, letting it drizzle down the sides.

Chill in the refrigerator for one hour before slicing.