Heat oil in a large soup pot over medium-low heat. Add onion and celery; cook and stir until tender, about 5 to 8 minutes. Add garlic, and cook for 30 seconds, continually stirring.
Stir in beans, chicken broth, pepper, thyme, and 2 cups water. Bring to a boil, reduce heat, and simmer for 15 minutes.
Use a slotted spoon to remove 2 cups of bean and vegetable mixture from soup; set aside.
Blend remaining soup in small batches in a blender at low speed until smooth — it helps to remove the center piece of the blender lid to allow steam to escape.
Pour blended soup back into pot; stir in reserved beans.
Bring soup to a boil, occasionally stirring. Stir in spinach and until spinach is wilted, about 1 minute.
Stir in lemon juice and remove from heat. Serve soup with freshly grated Parmesan cheese on top.
