Heat oil in pot over medium (4 quart) heat. Add onion and celery and sauté until onion is translucent, about 5-8 minutes.
Add broccoli, potato, bullion and water. Bring to boil.
Simmer uncovered until broccoli and potato is tender, about 15 minutes. With an immersion blender or regular blender, puree the soup. Put back in pot and add milk until heated and serve with shredded cheddar cheese, about 2 Tablespoons per person.