Heat a large pot to medium high. Add olive oil and onion and cook until onion is fragrant, 4-5 minutes.
Add zucchini, yellow squash and mushrooms and sauté for 10 minutes. Add garlic cloves and stir for about a minute.
Add tomatoes, broth and oregano. Bring to a low boil, reduce heat and then simmer for 15 minutes. Gently stir the beans and escarole/kale into soup and cook for another 5 minutes or until beans are heated through and greens are wilted. Serve with freshly ground pepper on top.