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1
Make Beurre blanc:
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2
Finely grate 1 tsp zest from a grapefruit. Squeeze 1/2 cup juice from a white grapefruit.
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3
Cut peel, including all white pith, from remaining fruit with a sharp paring knife and cut segments free from membranes. Chop enough grapefruit segments (use all colors) to measure 1/2 cup. Reserve 1 cup of remaining whole segments.
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4
Boil juice, wine, shallot, and vinegar in a small heavy saucepan until reduced to about 1 Tbl. Reduce heat to low and whisk in butter 1 piece at a time, lifting pan from heat occasionally to cool sauce and adding each new piece of butter before previous one has melted completely (sauce must not get hot enough to separate).
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5
Stir in chopped grapefruit and season with salt and pepper. Keep beurre blanc warm in a metal bowl set over a saucepan of hot water.
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6
Cook fish and vegetables:
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7
Preheat oven to 250 degrees F. Pat halibut dry and season with salt and pepper. Heat 1 1/2 Tbl oil in a large nonstick skillet over moderately high heat until hot but not smoking, then saute fish, in batches, if necessary, turning over once, until golden brown and just cooked through, about 5 minutes total. Transfer fish to a shallow baking pan and keep warm in oven.
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8
Wipe skillet clean and heat remaining 1 1/2 Tbl oil over moderately high heat until hot but not smoking, then saute mushrooms with salt and pepper to taste, stirring, until golden brown, 5 - 7 minutes. Add endives and saute, stirring, until leaves are slightly wilted, about 1 minute. Stir in reserved whole grapefruit segments and remove from heat.
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9
Serve fish over mushrooms, topped with beurre blanc and zest.