without having a casserole dish what is the best way to cook braising steak?
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You can use any wide, oven-safe pan or dish -- a large stainless steel or cast iron skillet would work, even!
With aluminum foil as a cover if the vessel doesn't have one of its own.
I would recommend a deeper pan - use you heaviest weight one. Then use parchment paper pressed right down on top of the food then the lid.