Heat the oven to 475F. In a 2 1/2-to-3-quart (ideally oven-safe) deep sauté pan, braiser, or shallow Dutch oven, heat the olive oil on medium-high. Add the onion, celery, and carrots.
Season well with salt and black or red pepper. Cook, sautéing, until the vegetables soften and brown lightly, about 10 minutes. Add the garlic, and cook for 1 minute more. Add the wine, if using, to scrape up any stuck bits, then simmer until it disappears, 1 to 2 minutes. Add the kale, and cook for 1 to 2 minutes, until collapsed, then add the tomatoes and bring to a simmer. Add the beans, and, if the mixture looks too dry or thick (canned tomatoes range quite a bit in juiciness), add up to 3/4 cup broth, 1/4 cup at a time. Simmer the mixture together over medium for about 10 minutes, adjusting the seasonings as needed.
If your pan isn’t ovenproof, transfer the mixture to a 3-quart baking dish. If it is, well, carry on.
Sprinkle the beans first with the mozzarella, then the Parmesan, and bake for 10 to 15 minutes, until browned on top. If you’re impatient and want a deeper color, you can run it under the broiler. Finish with parsley, if desired.
Serve with toasted garlic bread, if desired (optional).