Melt the butter in an ovenproof skillet or casserole with lid. Add the onions and cook, stirring occasionally with a two-pronged fork. As onions are stirred, the slices will separate into rings. Cook until onion rings are golden brown.
Sprinkle the onion with the flour and stir around briefly. Add the beef broth, stirring constantly. When the mixture bubbles up and is thickened, add salt and pepper. Onions naturally contain a good deal of sugar. To counterbalance this, add the vinegar. Partly cover with a lid and simmer for 15 minutes.
Add the beef slices and stir them around in the gravy until they are covered. Put the lid on and cook over low heat for about 30 minutes. Serve with bouillon potatoes.