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1
Preheat oven to 375u00b0F. Heat oil in a medium ovenproof saucepan over medium. Add onion, season with kosher salt and pepper, and cook, stirring occasionally, until translucent and softened, 5-8 minutes. Add rice and stir to coat; cook, stirring occasionally, until rice is translucent, about 5 minutes. Add bay leaf and 3 cups water; season with kosher salt and pepper. Bring to a simmer. Cover and bake in oven until rice is tender and water is absorbed, 15-20 minutes.
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2
Remove rice from oven and let sit 5 minutes, then gently fluff with a fork. Top with butter; let it melt into rice, then sprinkle with fleur de sel.
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3
Cook 1 cup unsalted butter in a small saucepan over medium, stirring often, until butter foams, then browns, 5-8 minutes. Remove from heat and slowly add cream (it will foam up slightly). Return to medium heat and cook, stirring often, until cream browns (mixture will go from pale beige to a deep caramel color), 5-8 minutes. At this point, sauce will look broken and grainy, but it will come back together. Remove from heat and stir in lemon juice and 1/2 cup water. Cut 2 tablespoons unsalted butter into small pieces. Whisking constantly, add butter a piece at a time, incorporating completely before adding the next piece, until sauce is glossy; season with salt and pepper. Keep sauce warm while you cook the fish.
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4
Place flour in a shallow baking dish. Season sole with salt and pepper, then dredge both sides of fillets in flour, shaking off excess.
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5
Heat clarified butter in a large skillet over medium-high until smoking. Carefully add fillets and cook until underside is golden brown, about 2 minutes. Gently turn fillets and cook until golden brown on the other side, about 1 minute. Add remaining 2 tablespoons unsalted butter and cook a minute or so until brown. Remove skillet from heat and, using a large spoon, baste fish with butter for a minute or two to finish cooking.
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6
Transfer sole to a platter. Spoon lemon cream sauce over; top with parsley. Serve with rice pilaf and lemon halves alongside.
