When it’s ready, lower the heat to medium and add the pieces of butter, stirring constantly. Once the butter is blended in, pour the half-and-half into the mixture VERY slowly. It will hiss and bubble and probably clump a little, but it will even out as you keep stirring. If you have large clumps, keep it on the heat and stir until they melt down a bit. Pour into a heatproof bowl and cool for about 10-15 minutes.