In a small saucepan, combine the sugar, flour and 1 teaspoon salt. Stir in milk until smooth. Cook and stir over medium-high heat until thickened and bubbly. Reduce heat; cook and stir 2 minutes longer.
Remove from the heat. Stir a small amount of hot mixture into egg; return all to the pan, stirring constantly. Bring to a gentle boil; cook and stir 2 minutes longer. Remove from the heat. Gently stir in vinegar and mustard. Cool without stirring to room temperature.
Cut potatoes into 1/2-in. cubes; place in a large kettle and cover with water. Bring to a boil. Reduce heat; cover and simmer for 8-10 minutes or until tender. Drain; rinse in cold water and drain again.
Set aside one hard-boiled egg for garnish; chop the remaining eggs. In a large bowl, combine the potatoes, chopped eggs, celery and onion. Whisk the mayonnaise, pepper and remaining salt into cooled milk mixture. Pour over potato mixture; toss gently to coat. Cover and refrigerate for at least 2 hours. Garnish with reserved egg.