In a large soup pot, heat the olive oil over medium heat. Add the pancetta, rendering the fat and cooking until slightly crispy about 3-4 minutes. With a slotted spoon, remove the pancetta and set aside for later.
Saute the onion, celery, carrot, zucchini, squash and garlic in the fat with a bit more olive oil if needed for 5 to 7 minutes. Season with salt and freshly ground black pepper, to taste.
Add the diced tomatoes, the drained kidney beans, cannellini beans, and the chicken or vegetable stock. Mix in the seasonings and bring to a boil. Reduce the heat to a simmer.
Add kale and the cooked pancetta and cook for another 20 minutes to allow flavors to combine. Use an immersion blender to partially puree the soup, leaving some chunks of beans vegetables for a creamier texture. Season with more salt and pepper if needed.
Serve with the grated cheese and crusty bread.