This was intended as a minimal dish, but, fair warning, it turned out to be far from it.
So my first two attempts ended with a pale yellow oily liquid. The third try yielded a thick glossy mayonnaise...the difference? Patience. You really do need to add the oil drop by drop right at the beginning, and then in a fine drizzle after that. Expect your drizzling arm to ache and your processor to start to overheat. It feels like forever while you're doing it, but it really only takes 10 minutes or so. Keep going! The result is so worth it.
Put the 2 yolks in the bowl of your small food processor. Add the salt and lemon juice and start the machine. With the oil in a measuring cup with a spout, drizzle in just a little oil, several drops at a time, while the machine is going. Keep finely drizzling in a few drops every 10 or 15 seconds and give the yolks a chance to incorporate the oil. Keep drizzling as slowly as you can and eventually after a couple of minutes you will see the mayo become pale and start to thicken. Continue drizzling slowly until all the oil has been incorporated. Store the mayo in an airtight jar in the fridge until you are ready to use it. Mix all the ingredients together. Taste as you go to get the exact proportions the way you like them. Refrigerate the dressing until you are ready to use it. Make it ahead to give the flavors a chance to develop and mingle.