Preheat the oven to 350°F. Lightly grease a 10-cup Bundt pan., To make the vanilla batter: Blend together the sugar, flour, salt and baking powder until combined., Add the butter, beating slowly with an electric mixer until the mixture is evenly sandy textured., Beat in the eggs one at a time, mixing until each egg is fully blended into the batter before adding the next. Scrape the bowl as necessary., Slowly add the buttermilk on low speed, then mix on medium speed until the batter is fully combined. It may appear slightly curdled; that's OK. Stir in the vanilla at the end., To make the chocolate batter: Mix the cocoa, espresso powder, baking powder, and water together until combined. Stir this cocoa paste into 1 cup (about 242g) of the vanilla batter., Pour half the vanilla batter into the prepared pan, and dollop with half the chocolate batter. Repeat, pouring the remaining vanilla batter into the pan, and dolloping with the remaining chocolate batter., Swirl the two batters together using a thin spatula or butter knife., Bake the cake for 40 to 45 minutes, or until a cake tester inserted into the center comes out clean, or perhaps with a few moist crumbs., Remove the cake from the oven, and cool it for 10 minutes in the pan before turning it out onto a rack., To make the icing: Mix the confectioners' sugar, cocoa, butter, and water to make a spreadable icing. Spread the icing on top of the slightly warm cake; it will slowly drip down the sides., Serve immediately, or within a day or so. Store the cake at room temperature; underneath a cake cover is ideal, but you can also tent it lightly with plastic wrap. Freeze for longer storage.