Separate the florets from the stems when cutting the broccoli into large pieces.
In a large soup pot, place the stems. Add 3 cups of water, potato, onion, and garlic. Cook for 10 minutes with the lid on.
Cook broccoli into the pot or until the broccoli is tender. Cook for another 15 when adding the collard greens and swiss chard. For 5 minutes when add the spinach. (See notes 1)
Puree the soup with a blender until it is smooth. The consistency should be moderately thick; thin with a little water if necessary. (See notes 2)
Mix 8 oz of chickpeas, lemon juice, 2 tsp dill, salt, and pepper to taste. Bring the soup back to a boil, then turn off the heat.
Whisk the 2 oz of water with tahini until smooth paste forms; stir into the soup.
To make the topping, combine the green peas, pomegranate seeds, the remaining chickpeas, and the remaining dill in a small bowl.
Pour the soup into bowls and top with 2 tbsp of the topping. Serve immediately.