Heat oil in Dutch oven over medium-high heat. Add onion, leek, carrot, and garlic; sauté for 5 minutes, stirring frequently. Add ham; sauté 2 minutes. Stir in water and next 7 ingredients (water through thyme); bring to a boil.
Cover, reduce heat, and simmer for 30 minutes. Add greens, beans, and tomatoes; bring to a boil. Reduce heat; simmer for 5 minutes. Discard bay leaves, and garnish each serving with cheese.