Bring a large pot of heavily salted water to a boil. When water boils, add greens and cook until wilted and tender, about 5 minutes. Drain and set aside.
Place bacon in a large frying pan and cook over medium-high heat, stirring occasionally, until browned and fat is rendered, about 3 minutes. Add onion and cook until softened, about 4 minutes. Add greens and turn to coat well. Add broth - it should cover greens and let cook until broth is reduced and greens are very tender, about 15 minutes. Season with salt and freshly ground black pepper and serve.