In a food processor fitted with the metal blade, a blender, or the jar of mayonnaise maker, combine the yolks, lemon juice, vinegar, mustard, salt, sugar, and cayenne. Pulse several times to blend.
With the processor running at high speed, or while quickly dashing the plunger of a mayonnaise maker, very slowly drizzle in the oil, allowing it to fully integrate as added until all the oil has been incorporated.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.
Recipe courtesy of Martha Hall Foose