Preheat the oven to 350° F
Lightly butter an 8 or 9-inch springform cake pan and line the base with a round of baking parchment.
In a pot of boiling, unsalted water, add the beets (whole and unpeeled). Cook until tender (~ 30-40 minutes)
Drain and rinse them with cool water. Slice off their stem, root, and peel them.
Process the beets in a blender or food processor until they're a coarse purée.
In a small bowl, sift together the flour, baking powder & cocoa.
Separate the eggs, putting the whites in a large mixing bowl and the yolks into a smaller bowl.
Gently whisk the yolks.
In a small bowl over a pot of simmering water, add the broken pieces of chocolate and allow it to melt. (Don't stir!)
When the chocolate looks like it's almost melted, pour the hot espresso over it and stir once.
Cut the butter into small pieces (the smaller, the better) and add it to the bowl with the melted chocolate.
With a spoon, push the butter below the surface of the chocolate, and allow to soften.
Remove the bowl of chocolate from the heat and stir until the butter has completely melted into the chocolate.
Let sit for a few minutes to cool before stirring in the egg yolks. After adding the yolks, mix until the eggs have blended into the mix.
Fold in the pureed beets.
Whisk the egg whites until stiff (it's far easier with a stand mixer), adding the sugar toward the end.
Fold the processed egg whites into the chocolate mix. (A large metal spoon is handy here; you'll want to work in deep, figure-eight movements, taking care not to over-mix.
Fold in the flour and cocoa mix.
Transfer the batter to the prepared cake pan and put in the oven, decreasing the heat immediately to 325 degrees F.
Bake for ~ 40 minutes.
How can you tell if it's done? The rim of the cake will feel spongy, while the inner part should still wobble a little when gently shaken. Test with a cake tester or toothpick too -- if it is still gooey in the center, continue baking just until moist crumbs cling to the tester.
Set the cake aside to cool (it will sink just a little in the center), loosening it around the edges with a thin icing spatula after half an hour or so.
The cake will be easiest to remove after it's completely cold.
Top with Ganache.
Coarsely chop the chocolate. (A serrated knife is best for the job; its saw-like teeth grab the chocolate, breaking it up)
Over medium-high heat, bring the coconut cream just to a boil.
Pour over chocolate, and add salt. Let stand for 10 minutes (don't stir -- as doing so will cool the ganache too quickly, and make it grainy)
Stir with a whisk until smooth and shiny to break up any pieces and emulsify the cream and chocolate.
Chocolate will often settle on the bottom or sides of the bowl. Scrape the dish with a rubber spatula to incorporate all of it.
To make a whipped filling or frosting: Let the ganache cool to room temperature, stirring often, 45 minutes to 1 hour. Beat it with a mixer on medium-high speed until paler and fluffy (~ 2 to 4 minutes)
This will yield about 2 cups.
Spread evenly over the cake