Preheat the oven to 350°F. Spread the bread pieces on a baking sheet and bake for 10-15 minutes, or until dry and slightly golden.
In a large pot, heat the olive oil over medium heat. Add the onion, celery, carrots, salt, pepper, dried thyme, and crushed red pepper. Cook, stirring occasionally, for about 10 minutes, until the vegetables are soft.
Stir in the minced garlic and cook for another minute. Add the white wine and let it reduce slightly, then add the tomatoes and vegetable broth. Bring to a simmer.
Add the cannellini beans and Parmesan rind, if using. Simmer for about 20 minutes. Stir in the kale and continue to simmer until the kale is wilted, about 5 minutes.
Stir in half of the toasted bread pieces. Let the soup simmer for another 5 to 10 minutes, or until the bread has absorbed some of the soup and thickened it. Stir in chopped parsley.
Ladle into bowls and top each serving with more toasted bread, a drizzle of olive oil, and grated Parmesan cheese.