Preheat your oven to 350 degrees F. Grease a 9×13-inch pan; set aside.
In a medium bowl, sift together the flour and baking soda, then stir in the salt.
Using an electric mixer, beat the butter and sugar on medium speed for 5 minutes, until light and fluffy. Scrape down the bowl, then add the vanilla and beat in the eggs, one at a time, until incorporated.
In another bowl, whisk together the hottest tap water, cocoa powder, and instant espresso powder until smooth. Add the half-and-half and whisk until smooth.
With the mixer on low, add the flour and chocolate mixtures alternately in thirds, beginning and ending with the flour.
Pour the batter into the prepared pan, smooth the top, and bake for 20 to 30 minutes, until a cake tester inserted in the center comes out clean. Cool completely in the pan on a wire rack before frosting.
Place the chocolate, butter, and espresso powder in a bowl. Pour the cream into a small saucepan and heat until it simmers. Remove from heat and pour over the chocolate mixture. Let stand for 1 minute, then stir until melted and smooth.
Refrigerate the ganache for 30 minutes. Beat with a handheld mixer on high speed for 15 to 20 seconds until soft peaks form.
Immediately spread on the cooled cake and serve.