Heat 4 tablespoons oil in large nonstick skillet over medium heat. Add garlic and dried crushed pepper; stir until garlic is pale golden, about 1 minute. Add the chopped stems and ribs and sauté for a few minutes until they soften.
Add greens by large handfuls; stir just until beginning to wilt before adding more, tossing with tongs to coat with oil.
Add 1 cup broth, cover, and simmer until greens are just tender, adding more broth by the tablespoonful if dry, 1 to 10 minutes, depending on type of greens.
Add beans; simmer uncovered until beans are heated through and liquid is almost absorbed, about 2 minutes. Stir in 1 teaspoon vinegar.
Season with salt and pepper, and more vinegar if desired; drizzle with remaining 1 tablespoon oil and serve.