Combine the dry mustard and vinegar in a bowl and let sit for 8-12 hours (I'll usually do this before bed and then make the mustard the next morning).

Beat the egg off heat in a medium saucepan and then add the sugar, salt, and mustard/vinegar mixture.

Cook over medium heat until thickened, remove from heat and let sit until cool.

Stir in the mayonnaise and mix until smooth (I prefer a wire whisk to remove lumps).

Pour into jars and refrigerate.