Heat olive oil in a skillet over medium heat. Add pancetta, leek, and garlic; cook and stir until browned, about 5 minutes.
Transfer pancetta and leek to a slow cooker; add chicken broth, kidney beans, potatoes, beef broth, tomatoes, carrots, green beans, corn, celery, parsley, black pepper, basil, and salt. Cook on Low until vegetables are tender, about 4 hours.
Transfer about half the vegetables from the slow cooker to a blender using a slotted spoon. Cover blender and hold lid down with a potholder; pulse a few times before leaving on to blend. Pour vegetable puree back into the slow cooker. Stir in garbanzo beans, cream, pasta, and 1/2 cup Parmesan cheese. Cook soup on High until flavors blend and pasta is cooked, about 1 hour.
Serve with remaining Parmesan cheese sprinkled on top.