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I'm not sure about the primal cut this comes from but if you have a much thicker(longer) piece then by all means cut it into 2 inch chops. Don't cut it longways with the grain, always cut across.
The braising pan should be sealed completely with parchment paper and foil. It should balloon up slightly in the oven so that the meat is actually almost pressure cooked. I'm not completely sure what purpose the parchment paper plays, my best guess is that aluminum is reactive and the braising liquid acidic.