In the bowl of a food processor, fitted with a metal blade, combine the egg, mustard, garlic and lemon juice. Season with salt and pepper. With the machine running, add the oil in a steady stream until the mixture is pale in color and thick. Remove from the processor and refrigerate for 1 hour.
*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.