Blanch (cook in boiling water for 3 minutes) broccoli. Drain off water. Cut off small florets and coarsely chop enough remaining broccoli stems to equal 2 cups.
Heat oil in a medium pot over medium heat. Saute the onion and celery until soft, about 5 minutes.
Whisk in flour and cook 1 minute. Add the broth and evaporated milk. Cook, stirring constantly, until the mixture simmers and thickens, about 5 minutes. If you don’t have enough evaporated milk to make soup creamy, add some regular milk, ½ cup at a time.
Add the chopped broccoli, cheese, pepper, nutmeg and salt, to taste. Stir until the cheese melts and the soup is heated through, about 3 minutes. Serve about 1 cup per person topped with broccoli florets. (Note: if using the 5 oz. evaporated milk, add another ½ cup of ‘regular’ milk to bring the amount of liquid to about 12 oz.).