Prepare the Cake:
Preheat your oven to 350°F (175°C). Line a 10×15-inch jelly roll pan with parchment paper and lightly grease it.
In a medium bowl, mix together the flour, cocoa powder, baking powder, baking soda, and salt.
In a separate bowl, beat the eggs and sugar together until thick and pale. Add the vanilla extract and mix well.
Gradually add the dry ingredients, alternating with the buttermilk, until just combined.
Spread the batter evenly into the prepared pan. Bake for 10-12 minutes, or until the cake springs back when lightly touched.
While the cake is still warm, invert it onto a clean kitchen towel dusted with cocoa powder. Carefully peel off the parchment paper.
Roll the cake up in the towel from the short side and let it cool completely.

Make the Coconut Pecan Filling:
In a saucepan, combine the butter, evaporated milk, sugar, and egg yolks. Cook over medium heat, stirring constantly, until the mixture thickens (about 10 minutes).
Remove from heat and stir in the vanilla extract, shredded coconut, and chopped pecans. Allow the filling to cool.

Assemble the Cake:
Carefully unroll the cooled cake. Spread the coconut-pecan filling evenly over the cake, leaving a small border around the edges.
Re-roll the cake without the towel. Place the roll seam-side down on a serving platter.

Decorate:
Spread any remaining filling on top of the roll. Garnish with toasted coconut, chocolate shavings, and whole pecans for an elegant touch.
Chill for at least 30 minutes before serving to allow the flavors to meld.