Adjust the oven racks to the upper-middle and lower-middle positions and heat the oven to 350 degrees. Grease three 8-inch round cake pans, then dust with cocoa powder and line the bottoms with parchment paper. Whisk the flour, baking soda, baking powder, and salt together in a large bowl. In a medium bowl, whisk the boiling water, chocolate, cocoa powder, and instant espresso together until smooth.
In a large bowl, beat the butter and sugar together with an electric mixer on medium speed until light and fluffy, 3 to 6 minutes. Beat in the eggs, one at a time, until incorporated, about 30 seconds. Beat in the sour cream and vanilla until incorporated.
Reduce the speed to low and beat in one-third of the flour mixture, followed by half of the chocolate mixture. Repeat with half of the remaining flour mixture, and the remaining chocolate mixture. Beat in the remaining flour mixture until just incorporated.
Give the batter a final stir with a rubber spatula to make sure it is thoroughly combined. Scrape the batter into the prepared pans, smooth the tops, and gently tap the pans on the counter to settle the batter. Bake the cakes until a toothpick inserted in the center comes out with a few crumbs attached, 15 to 20 minutes, rotating and switching the pans halfway through baking.
Let the cakes cool in the pans for 10 minutes. Run a small knife around the edge of the cakes, then flip them out onto wire racks. Peel off the parchment paper, flip the cakes right side up, and let cool completely before frosting, about 2 hours.