How to Make It
Soak the red and navy beans overnight. Drain and rinsed the soaked beans and transfer to a large pot, covering the beans with fresh cold water, about 10 cups. Simmer gently for 20 minutes. Add the potatoes and cook for another 10 minutes. Add the zucchini, globe squash, fava beans, peas, green beans, yellow wax beans, and leek scapes and cook for another 10 minutes. Add additional cool water to cover the vegetables as needed and continue cooking until beans are soft and cooked through, about 20 more minutes. Add the pasta and cook until al dente, about 10 minutes. Season to taste with salt and pepper.
Meanwhile, make the pesto. Mash the garlic cloves, pine nuts, and basil in a mortar with a pestle until a paste forms. Add the parmesan and mash. Stir in the extra-virgin olive oil and add kosher salt to taste. Set aside.
Ladle soup into individual serving bowls and stir in pesto to taste. Garnish with tomatoes and shaved parmesan.