Wash greens and pat dry. If using kale, collards, or chard, remove large center ribs. Chop leaves coarsely. Set aside.

Place a large, heavy skillet over medium heat. Add oil; once hot, add onion, garlic, and sage and sauté 6–8 minutes, stirring frequently, until onions are softened. Add greens and salt; stir to coat. You may need to add greens in two or three additions, waiting until they wilt down before adding more. Cook 3 more minutes, stirring occasionally; then stir in water or broth, tomatoes, and beans. Cover and simmer 3 more minutes, or until greens are tender but still green. Remove from heat, stir in lemon juice, and season to taste with sea salt and freshly ground black pepper. Divide among bowls and serve topped with Parmesan cheese (if using) and a generous drizzle of extra-virgin olive oil.