Soak the red and navy beans overnight. Put the soaked beans in a large pot of cold water, place on heat and cook 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, leek scapes, and elbow pasta and cook for another 10 minutes.
Make the pesto. Grind the garlic cloves, pine nuts, and basil in a mortar with a pestle until a paste forms. Add the parmesan and grind. Stir in the extra-virgin olive oil and add kosher salt to taste.
When the soup is finished, adjust the seasoning to taste. Add tomatoes and stir in pesto sauce to taste.
Garnish with shaved parmesan