Preheat the oven to 350°F. Prepare three 6-inch cake pans by buttering the insides and lining the bottom with a piece of parchment paper.
Create a double-boiler by filling a medium pot one-third of the way full with water. Place a medium stovetop-safe bowl atop the pot. Bring to a simmer over medium-low heat. Rough chop the chocolate into small pieces and drop it into the bowl atop the double-boiler. Occasionally move the chocolate as it melts. Once melted and glossy, remove from heat and reserve half for frosting.
Melt the butter in a small pot over low heat or in a microwave-safe bowl. Set aside.
Sift together the flour, granulated sugar, cacao, baking soda, baking powder, and salt in a large bowl.
In a stand mixer using the whisk attachment, combine the warm butter and brown sugar. Whisk on medium-low until the brown sugar has dissolved. Add the eggs one at a time, mixing until emulsified. Add the melted chocolate and mix on high speed for 1 minute, then add the vanilla extract.
In 3 batches, alternate pouring in the dry ingredients and buttermilk, beating on low and scraping down the sides. Gather ¼ cup warm water from the pot of the double boiler and mix until fully incorporated.
Pour the batter equally amongst the pans and bake for 30 to 35 minutes, until a toothpick comes out clean. Allow to cool atop a wire rack until fully cooled.
Frost the cooled cake with the chocolate buttercream.
For the Chocolate Buttercream: In a stand mixer using the paddle attachment, beat together the butter, cacao powder, and salt on medium speed until cohesive. Add the confectioners’ sugar, 1 cup at a time, mixing on low. Pour in the reserved melted chocolate and beat on medium for 1 minute. Then, pour in the whipping cream and beat on high for 3 minutes.
