Combine the dry mustard and vinegar in a bowl and let stand for 8-12 hours (I’ll usually do this before I go to bed). Beat the egg (I do this in a medium saucepan off heat so I make fewer dirty dishes), and then add the sugar, salt, and mustard/vinegar mixture. Cook over medium heat until thickened. Cool and then stir in the mayonnaise. Pour into jars and keep refrigerated.