Preheat the oven to 350ºF. Cut a piece of parchment paper large enough to cover the bottom and sides of an 8-inch loaf pan. Grease one side of the parchment, and fit it (ungreased side down) into the pan.
Add the chocolate and butter to small pot. Turn the heat to low, and let cook gently, stirring occasionally, until butter and chocolate are melted. Alternately, you can add the chocolate and butter to a medium, microwave-safe bowl. Cook on high power in the microwave in 30-second intervals, stirring in between each cycle, until the chocolate and butter are melted. Be careful not to burn the chocolate. The timing depends on the wattage of your microwave.
Stir in the vanilla extract; set aside to cool slightly.
In a small bowl, whisk together the flour, cocoa, and salt; set aside.
Add the egg, espresso, and sugar to a clean, large bowl. Whisk until well mixed and espresso is mostly dissolved. Whisk in the melted chocolate mixture. Using a rubber spatula, fold in the flour mixture.
Pour the batter into the prepared pan, spreading it evenly to the sides. Give the pan a tap on the counter to help it settle, too. Bake for 23 to 25 minutes until the center is set and the edges gently pull slightly away from the sides of the pan. Let cool completely before cutting.