In a large pot or Dutch oven combine 2 tablespoons olive oil, onion, garlic. Cook over medium heat, stirring often, until onion is translucent.
Add celery, carrot, parsley and winter squash or potatoes and sauté until vegetables begin to color, about 5 minutes.
Add tomatoes, Piment d’Ville, oregano, and broth and bring to a boil. Simmer until vegetables are tender, about 10 minutes.
While soup simmers, prepare croutons. Add olive oil and garlic to a large nonstick or cast iron skillet over medium heat.
Add bread and stir to coat with garlic oil. Cook, stirring and tossing frequently, until bread is browned and crisp on all sides, about 8 minutes. Reduce heat to low, scoot bread to one side of the pan to create an empty area.
Add butter and Piment d’Ville to that area and stir the two together. When the butter has taken on a bright red color, stir butter and bread together to coat. Season with salt to taste and remove from heat.
While croutons cool, add greens and beans to soup and season with salt. Cook until greens are tender, about 5 minutes.
Serve ladled into shallow bowls. Top with Parmesan and croutons.