Preheat the oven to 375°F, and lightly grease an 8″ round cake pan. Cut a piece of parchment paper to fit, grease it, and lay it in the bottom of the pan. See “tips,” below.
To make the cake: Put the chocolate and butter in a microwave-safe bowl (I use a quart-size Pyrex measure*), and heat until the butter is melted and the chips are soft. (Two 60-second bursts usually is sufficient in my microwave.) Stir until the chips melt; reheat briefly if necessary.
Stir in the sugar, salt, espresso powder, and vanilla.
Add the eggs, beating briefly until smooth. (I use a handheld beater.) Add the cocoa powder, and beat just to combine.
Spoon the batter into the prepared pan.
Bake the cake for 23-25 minutes; the top will have formed a thin crust, and it should register 200°F on an instant-read thermometer inserted into its center.
Remove the cake from the oven, and cool it in the pan for 5 minutes.
Loosen the edges of the pan with a table knife, and turn it out onto a serving plate. (The top will now be on the bottom; that’s fine. Also, the edges may crumble a bit, which is also fine.) Allow the cake to cool completely before glazing.
To make the glaze: Combine the chocolate and cream in a microwave-safe bowl, and heat until the cream is very hot, but not simmering. Remove from the microwave, and stir until the chocolate melts and the mixture is completely smooth.
Spoon the glaze over the cake, spreading it to drip over the sides a bit. (I use most but not all.) Allow the glaze to set for several hours before serving the cake.