In a large, heavy pot, combine the broth, squash, thyme, garlic, leeks, and celery and bring to a boil. Cover and simmer over low heat for 45 minutes.
In a medium skillet, heat the vegetable oil. Add the bacon strips and cook over moderately high heat, turning once, until crisp, about 7 minutes.
Discard the thyme sprigs from the soup. Working in batches, puree the soup in a blender. Return the soup to the pot. Add the bacon, collards, pinto beans, carrot, bell pepper and corn and bring to a boil. Simmer over moderately low heat, stirring occasionally, until the vegetables are tender, about 7 minutes. Season the soup with salt and pepper and serve.
