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1
Begin by removing the outer mottled gray membranes and any dark red portions from the monkfish fillets. On a slight angle, slice the fish into 1/2-inch thick medallions. Using two pieces of wax paper, place a few medallions between the paper and lightly pound them with the flat side of a meat mallet or small heavy saucepan to slightly flatten them.
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2
In a 4-5 quart saucepan, add the potatoes and enough cold water to cover them by 3 inches, season with salt and bring to a boil.
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3
Reduce heat to a gentle boil and cook 10 minutes.
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4
Trim the root ends and dark green leaves from the leeks. From the greens of one leek, trim any yellow, wilted or bruised parts and reserve them. The other two leek greens can be set aside for another use, like stock. Slice the leek whites and reserved greens in half lengthwise. Rinse layers well under cold water to remove any grit from between the layers. Using one set of leek whites and greens, cut again in half lengthwise. The remaining leek whites cut crosswise into 1 inch pieces. Add all the leeks to the potatoes after they have cooked at a gentle boil for 10 minutes. Cook leeks and potatoes for an additional 10 minutes or until they are tender.
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5
Reserve 2 cups of the potato/leek cooking liquid. Drain the remaining liquid from the vegetables. Transfer to a blender the leek greens, long pieces of leek whites and two slices of the potato. Add approximately 1/2 cup of the reserved cooking liquid and blend until smooth. While the blender is still running, add 1/2 cup of the olive oil in a thin steady stream. Blend until creamy and the sauce is thick enough to lightly coat a spoon. If necessary, add more cooking liquid to get the sauce to that stage. Strain the sauce into a small saucepan, keep warm over low heat.
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6
In a large skillet over a medium-high flame, heat 3 tablespoons of the olive oil. Add the remaining leeks and potatoes that have been drained and the thyme sprigs to the skillet.
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7
Season with salt and pepper and cook until golden brown, turning often, for approximately 12 minutes. Remove from heat and cover skillet to keep the mixture warm.
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8
Sprinkle the monkfish slices with salt and lightly coat them with flour, tap off excess. In a large non-stick skillet over medium flame, heat the remaining 3 tablespoons of oil. Add as many monkfish slices as possible to fit in a single layer. Cook fish only turning once until golden brown on both sides, approximately 5-7 minutes. Remove to a plate and keep warm.
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9
Divide the potatoes and leeks among 6 warm dinner plates. Place the monkfish slices on top of the vegetable mixture and spoon the sauce over the fish. Garnish with a sprinkle of parsley and/or chives. Serve immediately.
