PIA--Check out a few osso buco or braised lambshank recipes for some nice braising liquids. Some cuts of meat are better suited for braising than others and, like slow roasting, a certain amount of internal fat is helpful. Very lean meat doesn't braise well. You'll also get better results in the oven.
Short ribs, beef shank, veal shank, lamb shank, pork shank if you can find it are probably the best choices for braising, but if you want to turn a fairly inexpensive cut into something special, a seven bone roast or other chuck roast would be perfect.
A braised brisket would be wonderful too but those are pretty pricey.
I'm thinking about braising corned beef next time I buy one.

I use a standard 6 inch deep half size steamtable pan for braising. The meat should be dredged in flour and browned in a heavy Dutch oven. Some of the flour should be stuck to the bottom when you are done. Deglaze the pan with wine, add a little olive oil and cook trinity or mirepoix (I prefer mirepoix) until tender, ad some tomato paste, stock, seasonings, bring it to a boil and pour it over the meat in the braising pan. Cover the braising pan first with parchment paper then seal it with foil. Put it in a 325 degree oven for two hours.


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