Heat the oil in a heavy large pot over medium heat. Add the onion, carrot, pancetta, minced garlic, salt, and pepper. Cook until the onion is golden brown and the pancetta is crisp, about 7 minutes. Add tomato paste and stir until dissolved. Add tomatoes and stir, scraping the bottom of the pan with a wooden spoon to release all the brown bits. Add the spinach, beans, herbs, stock, bay leaf, and Parmesan rind. Bring the soup to a boil, reduce heat and simmer for 30 minutes.
Meanwhile, preheat the oven to 350 degrees F.
Drizzle the ciabatta halves with olive oil. Toast until golden brown, about 5 minutes. Remove from the oven and rub the top of the toasts with the whole garlic clove. Place the toasts in the serving bowls and ladle the soup over the toasts. Sprinkle with Parmesan and serve immediately.