Prepare the Whole-Grain Foundation. If your bread is fresh, preheat oven to 175°C (350°F). Scatter torn whole-wheat sourdough on a baking sheet and bake 15–20 minutes until completely dry and crisp.
Bloom the Aromatic Base. In a Dutch oven, heat 3 Tbsp extra-virgin olive oil over medium. Add onion, leek, and carrots; cook 12–15 minutes, stirring occasionally, until very soft and sweet.
Infuse the Herbs and Spices. Add garlic, rosemary, thyme, and red pepper flakes; stir constantly 1 minute. Deglaze with white wine, scraping up browned bits; reduce by about half.
Build the Savory Broth. Stir in undrained diced tomatoes, vegetable broth, cannellini beans, Parmesan rind, and bay leaf. Bring to a gentle boil, then reduce to a low simmer.
Simmer and Meld. Cover and simmer 25 minutes to infuse and meld flavors.
Wilt the Greens. Uncover; remove and discard Parmesan rind and bay leaf. Stir in kale; cook 5 minutes until tender and dark green.
Thicken and Finish. Turn off heat. Stir in half of the toasted sourdough until it begins to break down and the soup lightly coats the back of a spoon. Season generously with freshly ground black pepper and stir in lemon juice.
Serve and Garnish. Ladle into bowls. Top each serving with remaining toasted bread, about 3/4 teaspoon grated Parmesan cheese, and a final drizzle of high-quality extra-virgin olive oil.