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In a large saute pan, heat the oil over moderate heat. Add the shallots and cook, stirring occasionally, until beginning to brown, 3 to 5 minutes. Add the curry paste and cook, stirring, until fragrant, about 30 seconds. Add the chicken broth, coconut milk, 1/2 teaspoon salt and simmer until reduced to 2 cups, about 5 minutes.
Season the halibut with 1/4 teaspoon salt. Arrange the fish in the pan and gently shake the pan so the fish is coated with the sauce. Cover and cook until the fish flakes easily with a fork, about 7 minutes.
Arrange a pile of steamed spinach in the bottom of 4 soup plates. Top with the fish fillets. Stir the cilantro, scallions, and lime juice into the sauce and season, to taste, with salt and pepper. Ladle the sauce over the fish and serve with rice.