In a large pot, boil 5 cups water with onion, carrots, celery, garlic and mushrooms to make homemade vegetable broth. Once boiling, bring to a simmer and cook for 30 minutes.
In batches, place equal parts spinach and vegetable broth, in blender or Vitamix and puree until smooth. Repeat with remaining spinach and broth. Place soup in original vegetable broth pot and heat. Add in olive oil and milk; whisk well.
Once soup is hot, ladle soup in bowls and top with cheese. Serve and enjoy!