Heat the chicken broth in a saucepan over medium heat, and stir in the can of corn. Let the mixture heat to a boil, stirring occasionally, and reduce heat to a simmer.
In a skillet over medium-low heat, melt the butter and cook and stir the celery and onion until tender, about 5 minutes. Stir in the flour, and cook and stir for about 2 minutes to remove the raw taste from the flour. Add the vegetable mixture to the saucepan, whisking in the flour to avoid lumps, and stir in the nutmeg. Let the soup return to a simmer.
Whisk the egg in a bowl until thoroughly beaten. Stir the soup slowly in a clockwise circular motion, and slowly pour the egg into the moving soup. Stir the egg lightly through the soup with a fork to produce egg strands, and sprinkle with black pepper to serve.