In a food processor or blender, blend the egg and lemon juice for 10 seconds.
With the processor running, slowly pour in the oil through the feed tube. Mixture should thicken. Add the pepper and salt and pulse once or twice to blend.
Transfer to an airtight container and refrigerate for at least 30 minutes before using. Best if used within 24 hours.
*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.