Heat olive oil in a pot over medium heat. Cook onion, garlic, celery, and carrots until tender, 6 to 8 minutes.
Stir in broccoli and chickpeas; cook about 2 minutes.
Add 4 cups water. Bring to a boil; reduce heat and simmer until vegetables are tender, about 10 minutes. Remove from heat. Dissolve miso in 2 tablespoons cool water and stir into soup. Season with salt.