For the cake layers

1. Preheat oven to 350 degrees F.
2. Prepare cake pans by buttering the inside of 3 (9-inch) round cake pans. Line bottoms of pans with rounds of parchment.
3. In a medium bowl, whisk together whole milk, melted butter, whole egg, egg yolk, vanilla, and almond extract. Set aside.
4. In the bowl of an electric mixture fitted with a paddle attachment, whisk together the sugar, flour, cocoa powder, baking powder, baking soda, and salt.
5. On low speed, slowly beat the milk mixture into the flour mixture until just combined. Scrape down the side of the bowl as necessary. Then beat the mixture on high speed for 1 minute. Reduce speed to low and beat in boiling-hot water until just combined (batter will be thin).
6. Divide batter among cake pans (about 1 1/2 cups per pan) and bake in upper and lower thirds of oven, switching position of pans and rotating them 180 degrees halfway through baking, until a tester comes out clean, 20 to 25 minutes total.
7. Cool cake layers in pans on cooling racks for 15 minutes. Run a thin knife around edges of pans and invert layers onto racks. Carefully remove parchment paper and cool layers completely before assembling the cake.

For the filling

1. Reduce oven temperature to 325 degrees F.
2. Spread coconut in a large shallow baking pan and pecans in another. Bake pecans and coconut in oven, stirring occasionally, until golden, 12 to 18 minutes. Remove pans from oven. Set aside.
3. Pour the dulce de leche into a medium size microwave safe bowl. Warm the dulce de leche in the microwave for about 30 seconds until it is easy to stir. Stir in coconut, pecans, and vanilla.

For the glaze

1. Melt butter in a 3-quart saucepan. Remove pan from heat and whisk in chocolate and corn syrup until smooth.
2. Transfer 1 1/2 cups glaze to a bowl and chill, stirring occasionally, until thickened and spreadable, about 1 hour. Reserve remaining glaze at room temperature in pan.

For assembly

1. Put 1 cake layer on a 9-inch cardboard cake round set on a rack set over a baking pan (to catch excess glaze). Drop half of coconut filling by spoonfuls evenly over layer and gently spread with a wet spatula. Top with another cake layer and spread with remaining filling in same manner. Top with remaining cake layer.
2. Spread chilled glaze evenly over top and side of cake. Heat reserved glaze in pan over low heat, stirring, until glossy and pourable, about 1 minute. Pour glaze evenly over top of cake, making sure it coats sides. Shake rack gently to smooth glaze.
3. Chill cake until firm, about 1 hour. Transfer cake to a plate.