Though some versions of the recipe indicate that the ingredients should be very cold, this version specifies that the egg should be room temperature. Further research into the effects of temperature on emulsions should be conducted.
Thoroughly mix together the mustard, sugar, salt, cayenne, and egg in a deep bowl. Whisk in the vinegar.
Slowly beat the oil into the mixture. Whip until smooth.
Made using apple cider vinegar and olive oil. Initial tastes only of olive oil, slightly bitter. Should use better oil or one with less flavor next time. Made about 1 cup.