In a large pot or Dutch oven, cook bacon over medium until just browned. Add onion and cook, stirring often, until softened, about 3 minutes. Add a dollop Dijon mustard; stir for 1 minute. Add collard greens. Stir until wilted. Add enough chicken broth to almost cover the greens and salt and pepper. Cover and simmer over medium-low, stirring occasionally, until greens are very tender, about 45 minutes. Stir in a spoonful apple cider vinegar. Season.