Step 1

Put the yolk and mustard in a medium bowl. Beat together with a whisk. Begin to add the oil in dribbles as you beat, adding more as each amount is incorporated. You’ll notice when a thick emulsion forms. Then you can add the remaining oil a little faster. Depending on how fast you beat, the whole process will take about 5 minutes. To make by machine: Put the yolk and mustard in a blender or food processor and turn the machine on. While it’s running, add the oil in a slow, steady stream. When an emulsion forms, you can add it a little faster (and scrape down the sides as necessary), until all the oil is incorporated.

Step 2

Stir in the pickles or capers by hand. Add salt and pepper, then stir in the vinegar. Taste and adjust the seasoning. Use immediately.