Heat oil on medium heat in a soup pot or Dutch oven. Gently sauté onion and celery for 3-4 minutes, until onion is softened. Add potato and chopped broccoli, followed by the broth and milk. Bring to a boil, then reduce heat, cover and simmer for 20 minutes, until vegetables are tender. Allow soup to cool slightly, then transfer to a blender in 2-3 batches, and blend until smooth. Return soup to pot and heat gently until ready to serve.