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1
Finely grate 1 teaspoon zest from a grapefruit.
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2
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.
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4
Chop enough grapefruit segments (use all colors) to measure 1/2 cup.
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5
Reserve 1 cup of remaining whole segments.
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6
Boil juice, wine, shallot, and vinegar in a small heavy saucepan until reduced to about 1 tablespoon.
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7
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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8
Stir in chopped grapefruit and season with salt and pepper.
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9
Keep beurre blanc warm in a metal bowl set over a saucepan of hot water.
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10
Preheat oven to 250F.
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11
Pat halibut dry and season with salt and pepper.
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12
Heat 1 1/2 tablespoons 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.
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13
Transfer fish to a shallow baking pan and keep warm in oven.
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14
Wipe skillet clean and heat remaining 1 1/2 tablespoons oil over moderately high heat until hot but not smoking, then saute mushrooms with salt and pepper to taste, stirring, until golden brown, 5 to 7 minutes.
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15
Add endives and saute, stirring, until leaves are slightly wilted, about 1 minute.
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16
Stir in reserved whole grapefruit segments and remove from heat.
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17
Serve fish over mushrooms, topped with beurre blanc and zest.
