Combine flour and sugar in a small heavy saucepan.

Gradually whisk in milk until smooth.

Cook and stir over medium-high heat until thickened and bubbly.

Reduce heat and continue to cook and stir for 2 minutes.

Remove from heat.

Temper the egg by stirring a small amount of hot mixture into it, then return the mixture back to the pan while stirring constantly.

Bring to a gentle boil, and cook while stirring for 2 minutes.

Remove from the heat and transfer to a bowl.

Allow the dressing to cool to room temperature without stirring.

Cover the surface of the dressing with waxed paper, and refrigerate until completely cooled.

Just before serving, combine chopped apples and celery in a large salad bowl.

Drizzle with dressing and gently toss to coat.

Sprinkle with quartered grapes and toasted walnuts.