Whisk the egg yolks in a large bowl until light. Slowly whisk in the vinegar, lemon juice, salt, white pepper, and mustard.
Beat in the oil, a few drops at a time, until 1/2 cup has been incorporated. (The mayonnaise should be very thick at this point.) Continue to beat in the oil, 2 tablespoons at a time. Season with hot pepper sauce and, if you like, more salt or lemon juice. Thin with the boiling water.
Store, tightly covered, in the refrigerator. Mayonnaise will keep five to six days in the refrigerator, but bring it to room temperature before using.