Bring the milk, coconut milk and goat's milk to a simmer over low heat in a small saucepan. Keep warm while you prepare the caramel.
Combine the sugar and water in a medium saucepan over high heat and cook (do not stir) until it becomes a deep amber brown color. Slowly whisk in the warm milk mixture and continue whisking until smooth; add the vanilla seeds and corn syrup. Bring to a boil, reduce the heat to medium and cook, stirring occasionally with a wooden spoon, until the sauce is reduced by half and is the consistency of a caramel sauce, about 55 minutes.
Once the sauce is reduced, remove from the heat and whisk in the cold butter, vanilla extract, salt and rum and whisk until combined. Transfer the sauce to a medium bowl and stir in the pecans and coconut. Let the frosting cool to room temperature, stirring occasionally before frosting the cake.
For the ganache:
Bring the cream to a simmer in a small saucepan over low heat. Put the chocolate into a medium bowl, add the hot cream and the corn syrup and let sit for 30 seconds. Gently whisk until smooth. Let sit at room temperature for 10 minutes before pouring over the cake.
For the chocolate cake:
Preheat the oven to 325 degrees F. Butter 2 (9-inch) cake pans and line the bottoms with parchment paper.
Whisk together the flour, baking powder, baking soda and salt in a large bowl.
Melt the 12 tablespoons of butter in a medium saucepan over medium heat. Whisk in the cocoa powder and cook for 1 minute. Remove from the heat, add the sugars and whisk until the sugar is dissolved. Add the coffee, buttermilk, eggs and vanilla extract and continue whisking until smooth and just combined. Slowly add the buttermilk mixture into the flour mixture until combined.
Divide the batter evenly between the 2 pans and bake on the middle rack until a toothpick inserted into the center comes out with a few moist crumbs attached, about 42 minutes. Let cool in the pans on a baking rack for 20 minutes. Then invert the cakes onto the baking rack and let cool for at least 1 hour before frosting. Slice each cake in half horizontally. Put 1 cake layer on a cake round or platter and spread 1/3 of the frosting evenly over the top, repeat to make 3 layers and top with the remaining cake layer, top side up. Pour the chocolate ganache over the cake and let sit at room temperature for at least 30 minutes before slicing.
For the coconut whipped cream:
Combine the heavy cream, coconut milk, sugar, rum and vanilla in a stand mixer and mix until soft peaks form. Slice the cake, top each serving with a dollop of whipped cream and garnish with some of the toasted coconut.