In a small heavy saucepan, bring the half-and-half to a bare simmer over medium-low heat. Remove from the heat.
Place the chocolate in a medium heatproof bowl. Whisk the half-and-half slowly into the chocolate. Add the vanilla and butter to the sauce and whisk until the butter is completely incorporated. 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