Preheat oven to 425 degrees. In ovenproof skillet or Dutch oven wide enough to hold the fish in one layer, warm butter and olive oil over moderate heat. Add leeks and season with salt and pepper.
Stir well, then cover, reduce to moderately low and cook, stirring occasionally, until leeks have softened, 10-15 minutes. Do not let them brown.
Cut endive halves crosswise into 1/4-inch-wide pieces. Stir endive and tarragon into skillet, season with more salt and pepper, cover and continue cooking until endive has softened slightly, 3-4 minutes.
Season halibut fillets on both sides with salt and pepper. Arrange them on the bed of vegetables and transfer skillet to the oven, uncovered. Bake until fish just flakes, 10-12 minutes. Divide vegetables and fish among 6 dinner plates. Top fish with a generous drizzle of olive oil and garnish with parsley. Serve hot.