This version is essentially a mayonnaise, and it’s particularly important to use a very mild-tasting olive oil. If your oil is at all bitter, or if you’re unsure, use a mixture of it and a more neutral-tasting oil, like canola.
Combine the shallots and the vinegar in a small bowl, and set aside to macerate while you prepare the rest of the sauce.
Put the egg in a small saucepan of barely simmering water, and bring it to a boil. Then reduce the heat and simmer for about 4 minutes. Drain, and put the egg in a bowl of ice water to cool completely.
When the egg is cool, crack and scrape it into a medium bowl. Add the mustard and a pinch or two of salt. Mash it all together, and then begin whisking in the oil, just a few drops at first, then gradually increasing the flow to a thin stream. Stop adding oil when the mixture is satiny and has lots of body, like – and I love that Judy Rodgers describes it this way – a hot fudge sauce. Stir in the herbs and capers. Add the vinegar and shallots, and adjust with salt to taste.
Serve with grilled fish or poultry, fried seafood, roasted potatoes, boiled shrimp, or asparagus, or – my personal preference – as the dressing for a fantastic potato salad.