Preheat the oven to 400°F / 205°C. Tear 1 ciabatta loaf into chunks, toss with olive oil and spread on a baking sheet. Toast for about 10 minutes, until golden.
Heat 3 tablespoons of extra virgin olive oil in a large pot. Cook 1 chopped red onion, 2 chopped celery stalks, and 3 chopped carrots over medium heat until soft. Add 6 minced garlic cloves for 30 seconds.
Add 800g of canned whole tomatoes, 1 cup of dry white wine, and 4 cups of vegetable broth. Bring to a simmer, crushing the tomatoes.
Drain and rinse 850g of canned cannellini beans. Blend one-third with a ladle of the soup. Add the bean purée, 1 Parmesan rind, about 1in / 2.5cm long, 2 thyme sprigs, 1 bay leaf, and 1 teaspoon of dried oregano to the pot. Simmer for 20 minutes.
Add the remaining beans and 450g of chopped kale, thick stems removed. Simmer until the kale softens. Stir in half the bread and simmer until tender and thick.
Remove the rind, bay leaf and thyme stems. Season with salt and serve with the remaining toasted bread.