1. Dissolve 3 tablespoons salt in 4 quarts cold water in large bowl or container. Add beans and soak, at room temperature, for at least 8 and up to 24 hours. Drain and rinse well.

2. Adjust oven rack to lower-middle position and heat oven to 250°F. Place mushrooms and 1/2 cup water in small microwave-safe bowl and cover with plastic wrap. Cut several steam vents in plastic with paring knife and microwave on high power, 30 seconds. Let stand until mushrooms soften, about 5 minutes. Lift mushrooms from liquid with fork and mince. Strain liquid through fine-mesh strainer lined with paper towels into medium bowl. Set mushrooms and liquid aside.

3. Heat oil in large Dutch oven over medium heat until shimmering. Add onion, celery, and carrots. Cook, stirring occasionally, until vegetables are softened and lightly browned, 10 to 16 minutes. Stir in garlic and cook until fragrant, about 1 minute. Stir in remaining 4 cups water, broth, bay leaves, soaked beans, and reserved mushrooms and cooking liquid. Increase heat to high and bring stew to simmer. Cover pot, transfer to oven, and cook until beans are almost tender (very center of beans will still be firm), 45 minutes to 1 hour.

4. Remove pot from oven and stir in tomatoes and greens. Return pot to oven and continue to cook until beans and greens are fully tender, 30 to 40 minutes longer.

5. Remove pot from oven and submerge rosemary sprig in stew. Cover and let stand 15 minutes. Discard bay leaves and rosemary sprig; season stew with salt and pepper to taste. If desired, use back of spoon to press some beans against side of pot to thicken stew. Serve, sprinkled with Parmesan cheese and lightly drizzled with olive oil.

Serves 8