Using A Food Processor: Fit a food processor with the steel blade and place the egg yolks, lemon juice, pepper, and salt in the bowl. Blend until smooth. While continuing to process, very slowly drizzle the oil through the feed tube. Continue until all of the oil is used and the mayonnaise thickens.

By Hand: Using a whisk, beat the egg yolks, lemon juice, pepper and salt until well blended. Slowly add the oil by the 1/2 tsp, whisking constantly. Continue until all of the oil is used and the mayonnaise is thickened.