Heat the olive oil in a large Dutch oven over medium heat; cook and stir the onion until softened and translucent, about 5 minutes. Stir in the carrot and garlic, and cook for 5 minutes more.
Pour in the chicken broth, water, and white wine; stir in the potatoes, rosemary, sage, and thyme. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until the potatoes are tender, about 20 minutes. Add the cannelini beans, kale, chile pepper, and black pepper, and simmer, covered, for 30 more minutes.
