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.
Place the chocolate and vanilla in a medium heat-proof bowl. Add the half and half and let sit for 2 minutes, then whisk until smooth. Serve slightly warm.
The sauce can be kept refrigerated in an airtight container for several days, but it must be returned to room temperature, or warmed gently in a warm water bath before serving.
Yield: 1 1/2 cups