Scald the half-and-half and butter in a small, heavy saucepan over medium heat. Remove from heat.
Place the chocolate and vanilla in a medium-size, heat-proof bowl. Add the hot half-and-half and let sit for 2 minutes; 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 before serving.)
Makes 1 1/2 cups