Adjust an oven rack to the middle position and preheat oven to 400 degrees. On a rimmed baking sheet, arrange bread slices in a single layer.
Bake until lightly toasted and dry, about 15 minutes. Flip and continue baking 5 minutes longer. Remove from oven, adjust an oven rack to the lower middle position, and increase temperature to 425 degrees.
Meanwhile, in a large pot or Dutch oven over medium-high heat, heat olive oil until shimmering. Add onion, carrots, celery, garlic, and a pinch of salt, and cook until vegetables are softened, about 10 to 12 minutes.
Stir in vegetable broth, cannellini beans, cauliflower, potato, zucchini, herbs, 1 teaspoon salt, and 1/2 teaspoon pepper. Bring to a boil. Cover, reduce the heat, and simmer until potatoes are tender, about 15 to 20 minutes.
Stir in kale and remove from heat. Season to taste with salt and pepper (I like an additional 1 teaspoon salt and 1/2 teaspoon pepper).
Layer bread on top of the soup, pressing down gently to submerge, until all the slices are added. Drizzle the top of the soup with olive oil. Bake until the bread is hot and the soup is bubbling, about 10 to 15 minutes. Remove from oven and garnish individual portions with Parmesan cheese.