Place the chopped chocolate in a medium bowl. In a small saucepan, bring the half and half, butter, and sugar to a boil, stirring constantly. Pour the heated mixture over the chocolate.
Let stand for 1-2 minutes, then stir until the chocolate is completely smooth. Add the vanilla, espresso powder and liqueur (if using), and stir to combine. Serve warm. If serving cool, sauce can be thinned with water--one teaspoon at a time. Cover and refrigerate for up to 2 weeks. Reheat over a low heat or in the microwave.