1. Combine egg yolk, lemon juice, vinegar, mustard, and 1/2 teaspoon salt in medium bowl. Whisk until blended and bright yellow, about 30 seconds.
2. Using 1/4 teaspoon measure and whisking constantly, add 1/4 cup oil to yolk mixture, a few drops at a time, about 4 minutes. Gradually add remaining 1/2 cup oil in very slow thin stream, whisking constantly, until mayonnaise is thick, about 8 minutes (mayonnaise will be lighter in color). Cover and chill.
*Can be made up to 2 days ahead. Keep chilled.
*To make a garlic aioli, add 1 minced garlic clove to the egg mixture.