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1
Preheat oven to 425F.
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2
Cut 1 fennel bulb half lengthwise into paper-thin slices with a mandoline or other manual slicer and toss with oil and salt and pepper to taste.
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3
Cut remaining fennel lengthwise into 1/3-inch-thick sticks.
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4
Heat 3 tablespoons butter in a well-seasoned 10-inch cast-iron or heavy nonstick skillet over moderately high heat until foam subsides, then cook fennel sticks in 2 batches with salt and pepper to taste over moderate heat, stirring occasionally, until tender and edges are golden brown, about 7 minutes.
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5
Transfer to a bowl with a slotted spoon, reserving skillet, and keep warm, covered.
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6
Halve chestnuts and add to skillet with 1 tablespoon butter and salt and pepper to taste.
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7
Cook over moderate heat, stirring occasionally, until golden brown, about 3 minutes.
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8
Transfer to bowl with fennel using slotted spoon, reserving skillet, and keep warm, covered.
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9
Blanch fig leaves in boiling salted water 2 minutes, then transfer to a bowl of ice and cold water to stop cooking and drain well.
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10
Trim stems from leaves.
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11
Pat fish dry and season with salt and pepper.
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12
Add 1 tablespoon butter to skillet and heat over moderately high heat until foam subsides.
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13
Sear fish in 2 batches, turning once, until golden brown, about 2 minutes, transferring to a plate.
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14
Melt remaining tablespoon butter in skillet, then remove skillet from heat.
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15
If not using fig leaves, drizzle pieces of fish with butter.
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16
If using fig leaves, arrange 1 leaf, smooth side down, on a work surface, then put a piece of fish in middle and drizzle with some of melted butter.
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17
Wrap fig leaf around fish to enclose it and secure with wooden toothpicks.
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18
Wrap remaining fish in same manner.
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19
Boil 1/2 cup sauce in skillet until reduced to about 1/3 cup, about 2 minutes.
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20
Stir in chestnuts and cooked fennel and transfer to a wide shallow heavy pot (with a tight-fitting lid) just large enough to hold fish in 1 layer.
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21
Top chestnut mixture with fish.
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22
Cover pot with lid and roast in middle of oven until fish is just cooked through, 12 to 15 minutes.
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23
While fish is roasting, heat remaining 1/2 cup sauce in a small saucepan over moderate heat until hot.
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24
Remove toothpicks and open fig leaves.
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25
Serve fish (with fig leaves) over chestnut mixture and scatter with raw fennel.
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26
Serve warm sauce on the side.
