Preheat oven to 325 degrees. Grease a tube pan, or a 9″ or 10” springform pan fitted with the tube insert, with vegetable shortening. Line the bottom of the pan with parchment paper cut to fit. Grease the paper. Dust the inside of the pan with flour and tap out the excess.
Stir together the espresso powder, vanilla extract, and hot water in a small bowl.
On a large sheet of parchment or wax paper, sift together the flour, cake flour, cocoa, baking powder, baking soda, and salt. In a medium size bowl, toss the chocolate pieces with about 1 Tbsp. of this flour mixture. Set both aside.
In the large bowl of your mixer, cream the butter on medium speed for 2 minutes. Scrape the bowl.
Pour in the granulated sugar in 3 additions, mixing for about 1 minute after each addition. Scrape the bowl frequently to ensure even mixing.
Add in all of the brown sugar and beat for 1 more minute. Scrape again.
One at a time, add in the eggs, beating for 45 seconds after each one. Scrape after each.
Blend in the espresso mixture.
On low speed, add in the sifted ingredients alternately with the sour cream (3 additions of flour and 2 additions of the sour cream). Scrape as needed.
Blend in the heavy cream.
Remove the bowl from the mixer and fold in the chocolate pieces well with a spatula.
Spoon the batter into the prepared pan and smooth out the top.
Bake the cake on the middle rack of your oven for about 70 minutes or more, until a toothpick inserted comes out clean and the cake starts to pull away just slightly from the sides of the pan.
Cool the cake in the pan on a rack for 10 to 15 minutes. Invert the cake onto another cooling rack, remove the parchment paper and invert the cake again so it’s right side up. Allow the cake to completely cool on the rack.
Place the chopped chocolate in a medium size bowl. In a heavy sauce pan, warm the heavy cream over a low flame. Do not let it boil. Pour all of the warm cream over the chocolate and let it sit undisturbed for a few minutes, then gently stir until all the chocolate is melted, completely blended in, and the ganache is smooth. Wait until the ganache is closer to room temperature before spooning or pouring it over the cooled cake. (Be sure to place the cake on a rack over a sheet pan, to catch the drips, before pouring or spooning on the ganache.)