Rinse collard greens. Trim and discard thick stems from bottom of collard green leaves and coarsely chop leaves.
Cook bacon, in batches, in an 8-qt. stock pot over medium heat 10 to 12 minutes or until crisp. Remove bacon with a slotted spoon, and drain on paper towels, reserving drippings in stock pot.
Add butter and onions to hot drippings in skillet. Sauté onion 8 minutes or until tender. Add collards, in batches, and cook, stirring occasionally, 5 minutes or until wilted. Stir in vegetable or chicken broth, apple cider vinegar, salt, pepper and 3/4 of the bacon.
Bring to a boil. Reduce heat to low, and cook, stirring occasionally, 15 minutes or to desired degree of tenderness. Drain, reserving 1 cup liquid.
While collards are cooking, make the Béchamel Sauce. Stir Béchamel Sauce into drained collard mixture. Stir in reserved cooking liquid, 1/4 cup at a time, to desired consistency. Transfer to a serving dish, and sprinkle with reserved bacon.