Season the monkfish with salt and pepper and set aside until ready to use.

Heat one tablespoon of butter in a large, non-stick skillet over medium heat and sauté the shallots and garlic for 1 minute. Add the mushrooms. Season with salt and pepper, reduce heat, cover and cook for about 8 minutes.

In a separate non-stick skillet, heat the olive oil over high heat and sauté the fish for about 2 minutes per side. Remove and cut into 1-inch strips.

Raise the heat on the mushrooms and add the wine. When it steams up, in just a few seconds, lower heat, toss in parsley, tarragon and remaining one tablespoon of butter. Stir with a wooden spoon for about 3-4 minutes, over high heat. Add the fish to the mushrooms. Cover and cook over medium heat to warm through, for about 3 more minutes, Remove, season with additional pepper and salt if desired and serve.