Add all wet ingredients (except the oil which is a liquid but isn't "wet") to the work bowl of a food processor along with the salt, mustard and sugar. Pulse 5 times. Turn processor on and add oil in a steady stream until incorporated. Keep at room temperature for 2 hours. Refrigerate for up to 1 week.
*RAW EGG WARNING
Food Network Kitchens suggest caution in consuming raw and lightly-cooked eggs due to the slight risk of Salmonella or other food-borne illness. To reduce this risk, we recommend you use only fresh, properly-refrigerated, clean, grade A or AA eggs with intact shells, and avoid contact between the yolks or whites and the shell.