1. Preheat the oven to 350°F. Grease two 9-inch round cake pans with melted butter. Line the bottoms with circles of wax or parchment paper and butter the paper. Dust the pans with cocoa powder, tapping out any excess. Set aside.
2. Melt the chocolate in a double-boiler over simmering water. Set aside.
3. Cream the butter and brown sugar together in a large bowl, using an electric mixer, until light and fluffy, about 5 minutes. With the mixer on low speed, add the eggs, one at a time, beating well after each addition. Stir in the melted chocolate.
4. Sift the flour, baking soda, and salt into another bowl. With the mixer on low speed, and alternating between the two, add the flour mixture (one third at a time) and the sour cream (1/2 cup at a time) to the chocolate mixture, starting and ending with the flour. Scrape down the sides of the bowl and beat on medium speed for 2 minutes. Add the food coloring and vanilla to the boiling water, then slowly add it to the batter. Continue mixing until combined, 1 minute more.
5. Pour the batter evenly into the prepared pans and bake until a pick inserted in the center comes out clean, about 25 to 30 minutes. Let the layers cool in the pans on wire racks for 10 minutes, then remove the layers from the pans and let them cool completely on the rack. Carefully peel off the paper.
6. To assemble the cake, place one cake layer, topside up, on a serving plate. Spread it with a third of the Old-Fashioned Chocolate Buttercream. Top with the remaining cake layer, topside up. Frost the sides and top of the cake with the remaining buttercream. This cake is best served at room temperature.