Blanch arugula; drain and cool in ice water. In a blender or food processor, grind arugula, 1 clove garlic, and 2 tablespoons olive oil. Season with salt and pepper and set aside.

In a large saucepan, heat remaining 2 tablespoons olive oil and add onions and sliced garlic; cook over medium-low heat until translucent, 10 minutes. Add squash and broccoli spigarello or rabe; cook until greens are wilted, about 8 minutes. Add stock or broth and bring to a simmer; cook about 10 minutes.

Once flavors have blended, add cannellini or garbanzo beans, butter beans, and haricot verts or string beans. Return to a simmer, then remove from heat. Add arugula paste and stir. Season with salt and pepper. Ladle soup into bowls and serve, garnished with Parmesan cheese and a drizzle of olive oil.