Julia Child's Cooked Egg Mayonnaise

Ingredients

• 2 tablespoons flour
• 1/2 cup water
• 1 large egg
• 2 hard-boiled egg yolks
• 1 tablespoon Dijon mustard
• 1/2 teaspoon salt
• 2 1/2 teaspoons wine vinegar
• 2 1/2 teaspoons fresh lemon juice
• 1 cup excellent olive oil or other fresh vegetable oil
• Several grinds of pepper, preferably white
• More seasonings as needed: salt, vinegar, lemon juice, etc.

Directions

1. Put the flour in a 2-quart stainless-steel saucepan. While whisking, pour in the water a little at a time until the mixture is smooth. Set the pan on the stove and bring it to a boil, whisking slowly and making sure you sweep the entire base of the pan. Let it bubble gently for 1/2 minute, still whisking; if it seems firm instead of very thick, beat in a few drops of water. Take the pan off the heat, add the egg to the middle of the sauce, and whisk quickly until it is fully worked in. Return the pan to moderate heat and bring it back to a boil for 15 seconds, whisking slowly. Transfer the sauce to a food processor.
2. To the processor, add the hard-boiled yolks along with the mustard, salt, vinegar, and lemon juice. Run the machine for 15 seconds, until the yolks are completely blended in and ready to help hold the emulsion. With the processor still running, start drizzling in the oil drop by drop. Once the mixture has begun to emulsify, which should be after about 1/3 cup oil has been added, switch to a very fine, steady drizzle. When you have added as much oil as you want and the mayonnaise looks thick and shiny, taste carefully and adjust with salt, pepper, and any other seasonings you think it needs.
3. Spoon the sauce into a covered container and refrigerate it; it will keep for at least a week.
4. If the mayonnaise breaks, whisk the separated sauce to even it out. In a separate spot, whisk a spoonful of the broken mayonnaise into a spoonful of mustard or mashed hard-boiled egg yolk. Once that small mixture is smooth, gradually whisk in the rest of the broken sauce, adding it bit by bit. It should become thick, glossy, and lovely again, though it may still release a little oil or turn slightly grainy as it sits. If you see a little oiliness and mild graininess rather than a fully liquid sauce, just whisk the mayonnaise again before eating, and it should tighten up well enough.