Preheat the oven to 350 degrees F. Butter the bottom and sides of two 9-by-2-inch round cake pans. Flour the pans and tap out the excess. Line the bottoms with parchment paper.
Put the cocoa powder and chocolate in a medium bowl. Pour in the boiling water and whisk until the chocolate is melted. Whisk in the sour cream. Let cool to room temperature.
Whisk the flour, baking soda and salt in a medium bowl. Beat the butter and both sugars in a large bowl with a mixer on medium-high speed until fluffy, 3 to 4 minutes. Beat in the eggs one at a time, then the vanilla. Reduce the speed to low; beat in the flour mixture in three batches, alternating with the cocoa mixture. Finish mixing with a rubber spatula. Divide the batter between the pans.
Bake the cakes until a toothpick inserted into the centers comes out clean, 35 to 40 minutes. Transfer to a rack and let cool 15 minutes in the pans. Loosen the edges with a knife and turn out the cakes onto the rack and remove parchment; let cool completely.