1. To prepare the fish: Halve the leeks lengthwise, then slice crosswise and transfer to a large bowl of water. Swish leeks to release any grit; lift from the water. Drain.
2. Melt butter in large skillet over medium-high heat. Add leeks and thyme, and cook, stirring, until wilted and liquid reduces, 6 minutes. Season with 1/2 teaspoon salt and pepper, to taste. Add cider, bring to a boil, and cook until almost dry, 4 minutes. Stir in heavy cream, boil until thick and it coats the leeks. Add brandy, cook down slightly. Remove from heat and stir in parsley.
3. Open fish and season well with salt and pepper. Spread leek mixture along flesh and close fish. Tie closed with kitchen twine (or cooked leek greens) at 4-inch intervals. Brush oil all over skin, season with salt and pepper.
4. Preheat the broiler to high (with convection broiler if you have it). Line a pan with foil and lightly brush with oil. Place the prepared pan in broiler and heat for 5-10 minutes.
Carefully lay the fish on the preheated pan. Broil fish until an instant-read thermometer inserted into thickest part registers 130 to 135 degrees F, about 10 to 12 minutes. Remove from oven and rest fish for 5 to 10 minutes before serving.
5. Stir all sauce ingredients together. Transfer fish to a serving platter, remove strings. Serve with sauce on the side.
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