Step 1 Whisk together the egg yolks, vinegar and mustard in a medium bowl until pale in color. Add the oil drop by drop, whisking constantly, until the mixture begins to thicken.
Step 2 Continue whisking in the oil more steadily now, until all the oil is incorporated. Important note: If the mixture begins to break, you can add a few drops of water to bring it back together. Season with salt to taste. Store in the refrigerator until ready to use; keeps for two days. Makes 3 1/3 cups.
Step 3Food processor method: Combine the egg yolks, vinegar and mustard in the bowl of a food processor. Process for 30 seconds, then very slowly drizzle the oil a few drops at a time. After pouring in half a cup, drizzle the remaining oil in a thin stream. Season with salt to taste.