In a large Dutch oven or heavy-bottomed soup pot, warm the olive oil over medium heat. Add the sliced garlic and sauté gently until fragrant and just beginning to turn golden—watch carefully to avoid burning.
Stir in the diced onion, leek, carrots, celery, squash, and turnip. Cook, stirring occasionally, until the vegetables begin to soften slightly, about 5 minutes. Keep the heat moderate to prevent browning, allowing the vegetables to gently sweat and release their aromas.
Pour in enough water to barely cover the vegetables, approximately 6 cups (1.5L). Add the chopped kale and the bouquet garni. Increase the heat to bring the mixture to a gentle simmer. Once it begins bubbling, reduce to a low simmer and cook uncovered for about 25 minutes, or until all the vegetables are meltingly tender.
Next, add the cooked beans along with their reserved cooking liquid (or water, if using canned beans). Stir in the cubed bread, mixing thoroughly so it absorbs the broth. Simmer for an additional 15 minutes, stirring occasionally. The bread will begin to break down, thickening the stew into a rustic, hearty consistency. If the mixture thickens too much, add water in 1/2-cup increments to loosen it to your desired texture.
Season generously with salt and freshly cracked black pepper. The finished ribollita can be served in one of two ways: as a thick, chunky soup with visible vegetables and broth, or cooked down further until it resembles a dense porridge.
For a unique variation, spoon some of the thickened stew into a nonstick 8-inch skillet greased with a bit of olive oil. Cook over medium-high heat, stirring frequently, until the mixture binds together into a golden, pan-seared cake. Carefully flip it if desired and serve browned-side up for a crispy twist.
No matter how it's served, finish each bowl or slice with a generous drizzle of good-quality olive oil, freshly ground black pepper, and a sprinkle of Parmigiano Reggiano, if using.