Combine the half-and-half and butter in a small heavy-bottomed saucepan over medium heat. Heat the mixture until a thin paper like skin appears on the top. Do not boil. Add the chocolate and vanilla and stir until the chocolate melts and the mixture is smooth.
Remove from the heat and let cool.
The sauce can be kept refrigerated for several days, but it must be returned to room temperature before serving.
Yield: 1 1/2 cups