Cut the garlic clove into halves and rub the cut sides over the inner surface of a small bowl. Reserve the garlic.
Whisk the mustard and vinegar together in the bowl. Season with salt and pepper.
Dribble the oil into the bowl in a slow steady stream, whisking constantly, until the dressing is creamy and thickened and all the oil has been incorporated.
Taste and correct the seasoning. Add the reserved pieces of garlic; cover the bowl and let the dressing stand at room temperature until you need it. Remove the garlic and rewhisk the dressing if necessary before using.