First, make the grapefruit white butter sauce:

Finely grate 1 teaspoon zest from a grapefruit. Squeeze 1/2 cup juice from a white grapefruit. Cut peel, including all white parts, 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.

Boil juice, wine, shallot, and vinegar in a small heavy saucepan until reduced to about 1 tablespoon. 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).

Stir in chopped grapefruit and season with salt and pepper. Keep sauce warm in a metal bowl set over a saucepan of hot water.

Next, cook the vegetables and fish. Preheat oven to 250F. Pat halibut dry and season with salt and pepper. Heat 1 1/2 tablespoons oil in a large nonstick skillet over moderately high heat until hot but not smoking, then saut 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.

Wipe skillet clean and heat remaining 1 1/2 tablespoons oil over moderately high heat until hot but not smoking, then saut mushrooms with salt and pepper to taste, stirring, until golden brown, 5 to 7 minutes. Add endives and saut, stirring, until leaves are slightly wilted, about 1 minute. Stir in reserved whole grapefruit segments and remove from heat. Serve fish over mushrooms, topped with beurre blanc and zest.