Puree green onions and garlic scapes in a food processor.
Heat oil in a large soup pot over low heat. Add the onion-garlic mixture and cook until it starts to dry out, 2 to 3 minutes.
Puree lettuce, chard, and kale in the food processor. Add to the pot and cook for 4 to 5 minutes. Pour in vegetable broth; season with savory, marjoram, salt, and pepper. Simmer until kale and chard are softened, 40 to 45 minutes.
Mix Greek yogurt and Italian seasoning together. Serve soup in individual bowls; garnish each with a generous dollop of the topping.