Preheat the oven to 375°F (190°C). Line a 10x15-inch jelly roll pan with parchment paper and lightly grease.

Toast the shredded coconut and chopped pecans separately in a 350°F oven for 6–8 minutes until fragrant—watch them closely so they don’t burn. Set aside to cool.

Separate the eggs into yolks and whites. In a large bowl, beat the egg yolks with the brown sugar and half the granulated sugar until thick and lighter in color (about 3–4 minutes).

Stir in the warm milk, melted butter, and vanilla.

In another bowl, whisk together the flour, cocoa, baking powder, and salt. Fold the dry mix gently into the yolk mixture until combined.

In a clean bowl, beat the egg whites to soft peaks. Gradually beat in the remaining granulated sugar until stiff peaks form but not dry.

Fold one-quarter of the whites into the batter to loosen it, then gently fold in the remaining whites until no streaks remain.

Pour the batter into the prepared pan and smooth the top.

Bake 12–15 minutes until the cake springs back lightly when touched and a toothpick comes out mostly clean.

While it bakes, lay a clean kitchen towel on the counter and dust it generously with powdered sugar.

As soon as the cake comes out, loosen edges with a knife and invert it onto the sugared towel.

Carefully peel off the parchment paper.

Starting at the short end, roll the cake up in the towel (this helps it “remember” the roll and prevents cracking). Cool completely on a rack while rolled.

In a medium saucepan combine evaporated milk, granulated sugar, beaten egg yolks, butter, and a pinch of salt.

Cook over medium-low heat, stirring constantly, until the mixture thickens and becomes golden—about 10 minutes.

Remove from heat and stir in vanilla, toasted coconut, and toasted pecans. Let cool to room temperature (the filling will thicken as it cools).

Unroll the cooled sponge gently.

Spread the coconut-pecan filling evenly, leaving a 1/2-inch border along one long edge.

Re-roll the cake (without the towel), wrap in plastic wrap, and chill at least 1 hour to set.

Heat the cream until steaming and pour over chopped semisweet chocolate. Let sit 1 minute, then stir until smooth. Stir in butter for shine.

Unwrap the chilled roll, place it on a serving platter, and drizzle the glaze over the top.

Garnish with extra toasted coconut and pecans.

Use a serrated knife and wipe the blade between cuts for cleaner slices.

Serve at room temperature for the best texture.