For the cake, preheat the oven to 350°F. Grease two 8-inch round cake pans. Line the bottom of the pans with parchment paper and dust the sides with flour, tapping out any excess.
Sift the flour, sugar, cocoa powder, baking powder and salt into a large bowl or the bowl of a stand mixer fitted with the paddle attachment. Add the butter and mix on low speed until the butter has been worked into the flour (it will seem dry and crumbly).
Add the eggs and vanilla and mix in slightly, then mix in the beets. Add the hot water while mixing on low speed, then increase the speed to medium high and continue to mix for 2 to 3 minutes, until the batter is thick and fluffy. Scrape the batter into the prepared pans, spread to level the batter and tap the pans on the counter to knock out any large air pockets.
Bake the cakes for about 35 minutes, until a tester inserted in the centre of the cake comes out clean. Cool the cakes in their pans for 30 minutes then turn them out onto a cooling rack to cool completely.
For the frosting, melt the butter in a medium saucepot, then whisk in the sugar and cocoa powder. Continue to whisk this over medium heat until the mixture begins to bubble, then whisk in the cream. Continue to whisk until the mixture returns to a simmer (gentle bubbles) and whisk for an additional minute. Remove the pan from the heat and stir in the vanilla and salt.
Cool the mixture (it will look like a thick fudge sauce) to room temperature, then chill for about 1 hour, stirring occasionally while chilling. This will set the frosting to a spreadable consistency.
To assemble, peel the parchment from a cake layer and place it on a plate or platter. Spread an even layer of frosting over the top of the cake and place the second cake layer on top. Frost the top and sides of the cake, spreading until smooth. Chill the cake to set, but pull the cake from the fridge an hour before slicing and serving.
The cake will keep for up to 4 days, refrigerated.