Preheat the oven to 275 degrees. Place six (8-ounce) ramekins in a roasting pan large enough to hold them completely flat.
In a large heatproof bowl, whisk together the egg, egg yolks, and sugar until just combined. Meanwhile, scald the cream in a medium saucepan. Off the heat, add the chocolate and espresso and whisk until the chocolate is melted. Slowly whisk the cream mixture into the egg mixture, then whisk in the coffee liqueur and vanilla. Transfer to a large measuring cup and pour into the prepared ramekins until full.
Place the pan in the oven and carefully pour enough of the hottest tap water into the pan to come halfway up the sides of the ramekins. Bake for 40 to 50 minutes, until the custards are set on the edges but still a little jiggly in the middle when gently shaken. Remove the custards from the water bath, cool to room temperature, wrap in plastic, and refrigerate until firm.
To serve, spread 1 tablespoon of sugar evenly on each custard. With a kitchen blowtorch held one inch from the surface of the crème, heat the sugar until it caramelizes evenly. Allow to cool for 5 minutes and serve.