Heat the half-and-half and butter not quite to a boil in a small heavy saucepan over medium heat. Remove from the heat.
Place the chocolate and vanilla in a medium heatproof bowl. Add the hot 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 up to 3 days; rewarm gently before serving.)