In a heavy 12 inch skillet melt 3 Tbs butter over medium high heat. Add the mushrooms and cood stirring only occasionally until well browned, 5 to 7 minutes. Add garlic and cook, stirring until golden and fragrant, about 45 seconds. Add vermouth, 3 Tbs parsley, vinegar, salt, and pepper and boil until the liquid is reduced by half, about 2 minutes.
Remove the pan from the heat, lightly season the cod with salt and pepper and add it to the pan, nestling the fillets into the mushrooms and spooning some of the mushrooms on top.
Bring the mixture to a gentle simmer over medium heat, cover the pan, reduce to medium low and simmer until just cooked through, 7 to 12 minutes. With a slotted spatula, transfer the fish to serving plates. Over low heat whisk the remaining 1 Tbs butter into the sauce. Spoon the sauce over the fish and serve sprinkled with the remaining 1/2 Tbs parsley.
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