Heat a soup pot over medium-high heat. Add the EVOO, about three turns of the pan, and the pancetta or bacon and render for 4 minutes. Add the rosemary, garlic, three quarters of the onion, carrots and zucchini and season with salt and pepper. Sauté the veggies for 7-8 minutes, then add the wine and deglaze the pot. Stir in the tomatoes and stock and turn up the heat.
When the soup boils, reduce to a simmer and stir in the bread and beans. Pile the greens into the pot and wilt them into the soup. Simmer the ribollita for 5-10 minutes, stirring the soup as it simmers, until it thickens to a dense stew-like consistency. A wooden spoon should be able to stand upright in the pot.
Turn off the heat, adjust the seasonings and ladle into shallow bowls. Top with grated cheese, an additional drizzle of EVOO and a spoonful of reserved finely chopped raw onion.