How to Make It
In a large pot, heat 2 tablespoons of the oil. Add the onion, cover and cook over moderate heat, stirring, until softened, 4 minutes. Add the squash, cover and cook, stirring, until lightly browned in spots but not tender, 5 minutes. Stir in the garlic and rosemary and cook until fragrant, 1 minute. Add the kale and cook, stirring, until wilted, 5 minutes. Add the stock, cover and simmer until the kale and squash are just tender, 8 minutes. Season with salt and pepper.
Meanwhile, bring a medium saucepan of salted water to a boil. Add the pasta and cook until al dente. Drain the pasta.
Add the pasta and navy beans to the soup and simmer until the soup is slightly thickened, about 5 minutes. Stir in the remaining 2 tablespoons of olive oil. Ladle the soup into deep bowls and garnish with shaved Parmigiano-Reggiano cheese. Serve with garlic toasts.
The kale-squash soup can be refrigerated for up to 3 days.