Gather the ingredients. Dice and peel the 4 potato and 4 carrots. Dice the 300 g celery and slice thinly 1 onion. Soak the 225 g green beans in cold. Shred 900 g green cabbage. Mince 3 garlic clove.
The Cooking
In a large stockpot, put in the 1/2 cup extra virgin olive oil, 45 g unsalted butter, minced 3 garlic clove and sliced 1 onion and turn on the heat to medium low. Cook in the uncovered pot until it becomes colored a pale gold, but no darker, around 4 minutes.
Add the diced 4 carrots and cook for 3 minutes, stirring twice. Then add the diced 300 g celery, and cook, stirring occasionally, for 3 minutes. Add the diced 4 potato, cook, stirring occasionally, for 3 minutes.
While the carrots, celery, and potatoes are cooking, remove the 225 g green beans from the cold water, rinse, snap off both ends, and dice them. If you used frozen diced beans, you can skip that step, Add the diced 225 g green beans to the pot and cook, stirring occasionally, for 3 minutes.
Continue to give all ingredients an occasional stir and, after another few minutes, add the shredded 900 g green cabbage. Continue cooking for 6 minutes.
Add the 1.5 L broth, the 800 ml peeled tomatoesand the 400 ml finely chopped tomatoes with their juice, and a sprinkling of salt. Remember to taste and correct for salt later on. Cover the pot, and lower the heat, adjusting it so that the soup bubbles slowly, cooking at a steady, but gentle simmer. Leave it to cook slowly for 30 minutes.
Add the drained 540 g canned Cannellini beans, stir well, and cook for at least another 30 minutes. Cook until the consistency is fairly dense. Minestrone is supposed to be thick and not too watery.
The Serving
When the soup is done, just before you turn off the heat, swirl in the grated 50 g Parmigiano Reggiano cheese, then taste and correct for salt.