Whisk together garlic, yolk, lemon juice and mustard in a small bowl.
Add oil, a few drops at a time to yolk mixture, whisking constantly until all oil is incorporated and mixture is emulsified. If mixture separates, stop adding oil and continue whisking until mixture comes together, then resume adding oil.
Season with salt and pepper.
Chill, covered until ready to use. Keeps well for up to a day.