For the Cake:

1. Preheat oven to 350°F (175°C). Line a 10×15-inch jelly roll pan with parchment paper and lightly grease it.
2. In a large bowl, beat egg whites until soft peaks form. Gradually add 1/2 cup sugar, beating until stiff peaks form. Set aside.
3. In a separate bowl, whisk egg yolks and remaining 1/2 cup sugar until thick and pale. Stir in vanilla extract.
4. Sift together cocoa powder, flour, salt, and baking powder. Gently fold the dry ingredients into the yolk mixture.
5. Fold the whipped egg whites into the batter in three additions until fully incorporated.
6. Spread the batter evenly in the prepared pan. Bake for 12-15 minutes, or until the cake springs back when lightly touched.
7. While the cake is warm, turn it onto a clean kitchen towel dusted with cocoa powder. Peel off the parchment and gently roll the cake with the towel. Let it cool completely.

For the Coconut Pecan Filling:

1. In a medium saucepan, combine evaporated milk, sugar, egg yolks, butter, and vanilla. Cook over medium heat, stirring constantly, until thickened (about 10-12 minutes).
2. Remove from heat and stir in coconut and pecans. Let it cool to room temperature.

For the Chocolate Ganache:

1. Heat the cream in a small saucepan until just simmering. Pour it over the chopped chocolate in a bowl. Let sit for 5 minutes, then stir until smooth.

Assemble the Cake:

1. Unroll the cooled cake gently. Spread the coconut pecan filling evenly over the surface, leaving a small border. Roll the cake back up tightly (without the towel).
2. Place the rolled cake seam-side down on a serving platter. Pour the chocolate ganache over the top, letting it drip down the sides.
3. Chill for 30 minutes to set the ganache before slicing and serving.