COMBINE all ingredients except the milk in a container that is just larger than the head of your immersion blender. Let it settle for a minute.
INSERT the head of your immersion blender just over the top of your egg yolk. Wait 10 seconds to settle again, then turn your immersion blender on high speed. Keep it at high speed and down at the bottom over your egg yolk for 10 seconds, as the sauce emulsifies (thickens).
SLOWLY, still running your immersion blender on high, move up and down through the mixture for about 1 minute — until mixture is creamy and thick.
ADD compatible milk, 1 tablespoon at a time, until you have reached your desired consistency.
STORE in the fridge in a sealed container for up to 2 weeks.