Butter the bottom of a 9-inch-by-13-inch baking pan, then line it with parchment paper. Butter and flour the entire pan.

Sift the flour, baking soda, and salt together in a bowl.

Add the hot tap water, cocoa powder, and espresso powder to a liquid measuring cup and whisk together. Add the half-and-half and whisk until smooth.

Place the sugar and butter into the bowl of an electric mixer fitted with the paddle attachment. Beat for 4-5 minutes on medium speed until light and fluffy.

Add the vanilla and eggs one at a time, mixing until incorporated and the batter is smooth.

Turn the mixer to low and add the flour and chocolate mixtures alternately in thirds, starting and ending with the flour mixture.

Pour the chocolate batter into the prepared pan and smooth the top.

Bake in a preheated oven at 350 degrees Fahrenheit for 25 to 35 minutes, until a cake tester comes out clean.

Let the cake cool completely in the pan for about 45 minutes.

Chop the chocolate for the frosting into ¼-inch pieces and place in a bowl with the butter and espresso powder.

Heat the cream to a simmer and pour it over the chocolate mixture. Stir until the chocolate melts.

Stir in the Kahlúa and vanilla until smooth. Cover and refrigerate for 30 minutes.

Beat the frosting with a handheld mixer until it forms soft peaks.

Flip the cooled cake onto a serving board, remove the parchment paper, and frost the cake evenly with a metal spatula.

Cut the cake into squares and serve.