Line a jelly roll pan with parchment paper and lightly grease it. Preheat the oven to 350°F (175°C). Dust a clean kitchen towel with powdered sugar.

Whisk egg yolks with granulated and brown sugars until thick and pale. Add in oil, melted butter, vanilla, espresso powder, and buttermilk.

In another bowl, sift flour, cocoa powder, baking powder, and salt. Fold the dry ingredients into the wet mixture until just combined.

In a clean bowl, whip the egg whites to soft peaks, then gently fold them into the batter in two additions.

Spread the batter evenly in the prepared pan. Bake for 10 to 12 minutes until the top springs back lightly to the touch.

Immediately loosen the edges, invert the cake onto the sugared towel, peel off the parchment, and roll the cake up with the towel from the short side. Let it cool completely in that rolled shape.

In a saucepan, combine evaporated milk, sugar, egg yolks, butter, and vanilla. Cook over medium heat, whisking, until it thickens and turns glossy.

Remove from heat and stir in toasted coconut and chopped pecans. Let it cool to a spreadable texture.

Gently unroll the cooled cake and spread a thin layer of coconut pecan filling over the cake, leaving a half-inch border from the edges.

Roll the cake back up, using a piece of parchment to help if needed. Wrap the rolled cake in plastic and chill for at least 1 hour.

Slice using a warm serrated knife for neat slices.