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.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.