Put a medium saucepan filled with a few inches of water on to boil over medium heat.
In a stainless steel or heat-resistant bowl, whisk together the egg yolks, mustard, vermouth, honey, and a pinch of salt. Set it over the pan of hot water over medium-low heat. Make sure the bottom of your bowl does not come into contact with the simmering water to ensure the egg mixture doesn’t curdle. Whisk constantly until the sabayon nearly triples in volume and turns a pale yellow, about 10 minutes.
The sauce will become thick enough to hold a ribbon: when you raise your whisk and let the sabayon pour off the end of the whisk back into the bowl, that ribbon of sauce should sit on the surface of the sabayon for a couple of seconds before melting back into the mixture. Turn the heat off but keep the bowl sitting on top of the saucepan to keep warm. Press a piece of plastic wrap against the sabayon to prevent a skin from forming.