Step 1

Preheat the oven to 325°F and set an oven rack in the middle position. Spray a 12-cup Bundt pan generously with nonstick cooking spray with flour, such as Baker's Joy or Pam with Flour.

Step 2

In a small microwave-safe bowl, combine the coffee and chocolate. Heat in the microwave on high power in 20-second intervals, stirring in between, until the chocolate is about 75% melted. Stir, allowing the residual heat in the bowl to melt the remaining chocolate, until the mixture is smooth. Set aside.

Step 3

In a medium bowl, whisk together the buttermilk, eggs, and vanilla. Set aside. (Note that the mixture may start to look curdled as it sits; that's okay.)

Step 4

In the bowl of an electric mixer fitted with the paddle attachment or beaters, combine the flour, cocoa powder, sugar, salt, baking powder, and baking soda. Beat on low speed for 30 seconds to combine. Add the softened butter and half of the buttermilk mixture and mix on low speed until moistened but still a little crumbly, about 1 minute. With the mixer running on low, gradually add the remaining buttermilk mixture until incorporated, then increase the speed to medium and mix for 3 minutes, stopping once to scrape down the sides and bottom of the bowl with a rubber spatula. The batter should look creamy. Scrape down the sides and bottom of the bowl again, making sure the batter is evenly mixed.

Step 5

Add the chocolate/coffee mixture and mix on low speed until smooth.

Step 6

Transfer the batter to the prepared Bundt pan and smooth the top with a spatula. Bake for 55 to 60 minutes, or until a cake tester comes out clean or with just a few crumbs.

Step 7

While the cake bakes, make the soaking syrup: In a small saucepan, combine the butter, sugar, water, and vanilla. Bring to a boil, then reduce the heat and simmer until the sugar is dissolved, about 1 minute.

Step 8

Set the cake pan on a cooling rack. Using a skewer or toothpick, poke about 40 holes in the bottom of the still-hot cake, going about three-quarters of the way down. It may deflate a bit during this process; that's normal. Spoon or brush half of the syrup evenly over the bottom of the cake. If the syrup starts to pool on the surface, poke more holes to help it absorb. Leave the cake on the rack to cool for 30 minutes.

Step 9

Invert the cake onto a serving platter. Brush the remaining syrup evenly over the top and sides of the cake, letting it soak in as you go. Let the cake cool completely, at least a few hours.

Step 10

Make the chocolate glaze: Add the butter to a small saucepan and melt over low heat. Remove the pan from the heat. Add the chocolate and whisk until melted. Add the confectioners' sugar and 2 tablespoons of the hot water and whisk until completely smooth. The glaze should be the consistency of warm honey so that it coats the top of the cake evenly and then cascades slowly down the sides. If the glaze is too thick, whisk in the remaining tablespoon of water, little by little, until you get the right consistency. If the glaze is too thin, whisk in a bit more confectioners' sugar. Using a small spoon, drizzle the glaze over the top of the cake, letting it drip down the sides. Allow the glaze to set before serving, at least 30 minutes. Slice the cake with a serrated knife. The cake will keep well in a covered container at room temperature for up to four days.