Whisk together cornstarch, mustard, sugar, salt and cayenne in a medium saucepan. Add 1/4 cup of the buttermilk and whisk until you have a smooth paste. Add egg and the remaining 1/2 cup buttermilk and whisk until smooth.Advertisement
Set the pan over medium-low heat and cook, whisking, until the mixture comes to a simmer and thickens. Continue to whisk for 15 seconds, then remove the pan from the heat.
Whisk in lemon juice and oil. Transfer the mayonnaise to a small bowl and press a piece of plastic wrap directly on the surface to prevent a skin from forming. Let cool.
Make Ahead Tip: Cover and refrigerate up to 3 days. Whisk before using.