Preheat the oven to 350°F (175°C). Line your jelly roll pan with parchment paper and lightly grease the paper.

Lay a clean, slightly damp kitchen towel on the counter and dust it with powdered sugar.

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

In a separate large bowl, beat the egg yolks with 1/2 cup granulated sugar until pale and slightly thick, about 2-3 minutes.

Add the oil and vanilla, mixing until smooth. Gently fold the dry ingredients into the yolk mixture.

With clean beaters, beat the egg whites and remaining 1/4 cup sugar until stiff peaks form.

Fold one-third of the egg whites into the yolk batter, then carefully fold in the remaining whites.

Spread the batter evenly in the prepared pan and bake for 10-12 minutes.

Immediately invert the cake onto the sugared towel and roll it up to cool.

Combine evaporated milk, brown sugar, butter, and egg yolks in a medium saucepan and cook over medium-low heat until thickened.

Remove from heat and stir in coconut, pecans, and vanilla. Let cool.

Unroll the cooled sponge and spread the filling evenly.

Re-roll the cake tightly without the towel and transfer seam-side down to a serving platter.

Place chocolate and corn syrup in a bowl. Heat the cream and pour over chocolate until smooth.

Drizzle over the roll and let it set.

Chill the roll for 1-2 hours. Slice with a sharp serrated knife.