Preheat your oven to 350°F for the croutons.
In a large pot over medium to medium-high heat, sauté the carrots, onion, celery, and fennel with plenty of olive oil. Season generously with salt and pepper. Cook the vegetables until they are caramelized, about 20 minutes, stirring frequently and making sure they don’t burn.
Once the aromatics are caramelized, add the tomato paste and cook it until it turns a deep rust color, stirring constantly so it doesn’t burn. This should take about 3 minutes.
Add the rosemary sprig and deglaze the pan with the white wine. Scrape up any browned bits stuck to the bottom of the pot. Let the wine simmer and reduce until most of the liquid has cooked off.
Add the water, kale, beans, parmesan rind, and potatoes. Season again with salt — make sure the soup is well seasoned. Stir to combine and ensure nothing is sticking to the bottom of the pot. Bring everything to a simmer and cook for 30–40 minutes. The potatoes will be very tender, almost falling apart, and the kale will be soft and a deep dark green.
While the soup cooks, make the croutons. Tear or dice the bread into bite-size pieces. Scatter them on a baking sheet, drizzle with olive oil, and season with salt. Bake for about 30 minutes, or until crisp and golden brown. Remove from the oven and let cool while the soup finishes cooking.
To finish the soup, remove the parmesan rind and stir in a spoonful of vinegar. The soup needs a touch of acid at the end to brighten the flavors. Taste and adjust the seasoning if needed.
To Serve: Ladle the soup into bowls and top with plenty of croutons. Finish with grated parmesan cheese, fennel fronds, freshly ground black pepper, and a generous drizzle of olive oil.