Season pork with salt and pepper. Dredge in flour, shake off excess. Melt butter with 1 tablespoon oil in heavy large deep skillet over medium-high heat. Add pork in batches and brown well, about 6 minutes per side. Transfer pork to plate. Set aside
Dredge onions in flour; shake off excess. Heat remaining 1 tablespoon oil in same skillet over medium heat. Add onions and garlic. Season with salt. Cover and cook 5 minutes, stirring once. Uncover and cook 4 more minutes, stirring occasionally. Add 1/4 cup stout and 3/4 cup stock and bring to a boil, scraping up any browned bits. Return pork to skillet. Spoon some of onions over pork. Add enough additional stout and stock to bring liquid halfway up sides of pork. Cover skillet with foil, then lid. Reduce heat and simmer 20 minutes. Turn pork over and cook until very tender, about 25 more minutes. Transfer pork and onions to platter using slotted spoon.

Degrease pan juices. Boil juices until thickend slightly, about 10 minutes. Whisk in 1 tablespoon mustard. Add chopped parsley and 1 1/2 teaspoons balsamic vinegar. Taste, adding more mustard or vinegar if desired. Pour gravy over pork. Garnish with parsley and serve.