Preheat the oven to 350 degrees. Brush a large rimmed baking sheet with half of the 1 tablespoon of melted butter. Line the pan with parchment paper, cutting a diagonal line from each corner into the corners of the pan so the paper nestles in easily. Brush the parchment and sides with the remaining 1/2 tablespoon of melted butter. Set aside.

Melt the butter in a medium sized microwave safe bowl until melted, about 45 seconds to 1 minute. Add the vanilla extract and stir to combine. Set aside.

Add the room temperature eggs, sugar, and salt to the bowl of a stand mixer and whisk just to combine with the whisk attachment. Beat the mixture at high speed until it triples in volume, about 5 minutes, or until you can draw a figure 8 by dipping the whisk attachment into the batter and it holds.

While the eggs and sugar are being whipped, combine the flour, cocoa, and espresso powder with a whisk until combined. Sift the mixture together three times. Sift 1/3 of the flour mixture into the egg-sugar mixture, and gently fold it in using a rubber scraper. Repeat with the remaining 2/3 of the dry ingredients, being careful not to over-fold. Add about 1 cup of the batter to the butter-vanilla mixture and mix gently until combined. Add this to the remaining batter and fold in gently just until incorporated. Pour large dollops of the batter over the entire surface area of the prepared pan so it's easier to spread without over-working. Spread as evenly as possible with an offset spatula, and bake on the center rack of the oven for 15-20 minutes, or until the top of the cake springs back when gently pressed and the cake pulls away from the sides of the pan. Cool 5 minutes on a wire rack.

While the cake cools, lay a large lint-free towel on the counter. Holding the cake pan with the cake facing away from you, hold onto the sides with oven mitts or towels and invert the cake gently onto the towel. Gently roll the cake up in the towel while it's still warm, and cool on the wire rack for 1 hour or until completely cool.

Place the cubed butter, coconut, and pecans in a medium bowl and set aside.

Place the heavy cream, sugar, and egg yolks in a medium saucepan and whisk to combine. Heat over medium heat, stirring constantly with a wooden spoon until thickened and the custard coats the wooden spoon and you can draw a line in the back of the spoon and it holds. Add the hot custard mixture to the bowl with the butter, coconut, and pecans, and stir until the butter has melted. The frosting will thicken as it cools.

Place the chocolate chips and heavy cream in a heat proof bowl. Set aside.

Fill a large sauté pan halfway full of water and heat over medium heat until the water simmers. Turn the heat down to low, then place the bowl of chocolate chips and cream, stirring constantly with a rubber scraper until the chocolate melts and emulsifies with the cream. When the mixture is smooth, remove from heat and set aside to cool.

Place the water and sugar in a small sauce pan over medium heat and stir until the sugar has melted. Add the instant espresso powder and stir until dissolved. Set aside.

Once the cake and frosting have cooled, unroll the cake and trim the edges with a sharp knife. Lightly dab the simple syrup onto the cake using a pastry brush. You will not need all of the syrup, just enough for a light coating. Spread the frosting evenly over the unrolled cake, leaving a border of 1" around the cake. Carefully roll the cake as tightly as possible, tucking it gently as you roll. Place on a serving plate with two pieces of waxed paper on either side, which will be removed after frosting with the ganache.

If the ganache has cooled too much, heat it in the microwave for about 20 seconds or until just pourable. Pour some of the ganache over the cake carefully -- you won't need it all -- and frost the sides with the ganache on the waxed paper. Garnish the cake with more sweetened, shredded coconut and pecans. Chill at 4 hours or until set. Enjoy!