Heat 2 teaspoons oil in a Dutch oven over medium-high heat. Add carrots, sweet potatoes, and onion; sauté 7 minutes. Stir in stock, 1 cup water, pepper, salt, and oregano and bring to a boil. Reduce heat, and simmer 20 minutes.
Stir in beans, kale, tomatoes, and Parmesan cheese; let stand 5 minutes.