I always saute it in olive oil and it falls apart on me. It ends up looking like mush. How do I get it to stay in one piece?
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You could try dredging it in Wondra before pan frying it at a highish heat and for that you might want to try a canola or vegetable oil that can handle a higher heat. Or you could lightly brush a baking pan and the the fish with some olive oil (plus S&P) and broil it for about 3-5 minutes.
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The simpler the better. With flounder be sure to use tweezers to remove any pin bones. But with either fish I would go with a saute in brown butter. Flounder will possibly have some skin that you will want to crisp up, so give it a dusting in Wondra or rice flour. You might add capers to your pan. After that it need little more than a salt and pepper and a squeeze of lemon. If you want to sauce it maybe a classic sauce gribiche.