Crab-Stuffed Sole Paupiettes with Sauce Vin Blanc

1. 1
   Melt the butter in a medium frying pan over medium heat until foaming. Add the shallot and cook, stirring occasionally, until softened but not browned, about 3 to 4 minutes.
2. 2
   Sprinkle in the flour, stir to coat the shallot, and cook until the raw taste has cooked off, about 1 minute. Whisk in the wine and simmer until the mixture has reduced slightly and thickened, about 1 to 2 minutes.
3. 3
   Whisking constantly, slowly pour in the cream and bring to a simmer. Continue simmering until the sauce has thickened and reduced by about a third, about 8 minutes.
4. 4
   Remove the pan from the heat and stir in the crabmeat, chives, lemon zest, lemon juice, salt, and pepper until combined (the mixture should be thick). Transfer to a large plate and spread into an even layer. Cover loosely with plastic wrap and refrigerate until completely chilled, about 1 to 1 1/2 hours.

For the fish and the sauce:

1. 1
   Heat the oven to 200°F and arrange a rack in the middle.
2. 2
   Place a fine-mesh strainer over a medium heatproof bowl and set aside.
3. 3
   Combine the water, wine, shallots, carrots, celery, parsley, and measured salt in a large straight-sided frying pan with a tightfitting lid and bring to a boil over high heat. Reduce the heat to medium and simmer until the poaching liquid has reduced by a third and the flavors have developed, about 20 minutes.
4. 4
   Meanwhile, place the sole fillets in a single layer on a work surface and lightly season both sides with salt and white pepper. Divide the chilled crab filling among the fish fillets, spreading it into a thin, even layer along the length of each fillet and leaving a 1/4-inch border. Starting with the thicker end, roll up each fillet. Place the fillet rolls seam-side down in a shallow baking dish, cover the dish with plastic wrap, and refrigerate.
5. 5
   Pour the poaching liquid through the reserved strainer and discard the contents of the strainer. Return the poaching liquid to the pan, bring it to a bare simmer over high heat, then reduce the heat to low. Reserve the strainer and medium heatproof bowl for later use.
6. 6
   Place the rolled fillets seam-side down in the poaching liquid and cover the pan. Poach at a low simmer until the fish is opaque and firm to the touch, about 18 to 20 minutes. Meanwhile, wash and dry the shallow baking dish and set it aside.
7. 7
   Using a flat spatula, carefully transfer the fish to the clean baking dish. Pour the poaching liquid through the strainer and discard the contents of the strainer. Pour 1/2 cup of the strained liquid into the baking dish. Cover with aluminum foil and place in the oven to keep warm. Line a plate with paper towels; set aside.
8. 8
   Pour 1 cup of the strained poaching liquid into a small saucepan and bring to a boil over medium-high heat. (If you have less than 1 cup of poaching liquid left, add enough water to make 1 cup.) Boil until the liquid is reduced to 3/4 cup, about 4 minutes. Meanwhile, mix the butter and flour together in a small bowl until a smooth paste has formed; set aside.
9. 9
   Reduce the heat under the poaching liquid to medium. While whisking, slowly add the cream and then simmer, whisking occasionally, until the sauce coats the back of a spoon and has reduced to 1 cup, about 3 minutes.
10. 10
    Whisk in the butter-flour mixture and simmer, stirring constantly, until the butter mixture is incorporated and the sauce has thickened, about 1 to 2 minutes.
11. 11
    Remove the pan from the heat and stir in the lemon juice. Taste the sauce and season with salt and pepper as needed.
12. 12
    To serve, spoon 2 tablespoons of the sauce onto a small plate. Place one paupiette on the towel-lined plate to remove the excess moisture, then place in the sauce. Repeat with the remaining paupiettes. Evenly drizzle the remaining sauce over the paupiettes and garnish each with 2 crossed pieces of chive. Serve immediately.