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1
Place the butter for the nut crust in a medium saucepan over medium-high heat. Cook for 4 minutes, until the butter is nutty smelling and golden brown. Remove from the heat and strain the butter through a fine-mesh sieve to remove any black bits.
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2
Add the pistachios, pine nuts, sugar, lemon juice, and 1/4 teaspoon salt. Mix well, then spread out in a small parchment-lined baking sheet, about 6 inches wide and 8 inches long. Chill in the fridge for 2 to 3 hours, until the butter has set firmly, then cut the mixture into 6 equal rectangles. Return the rectangles to the fridge until ready to use.
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3
To make the vichyssoise, bring a medium saucepan of salted water to a boil and add the parsley and arugula leaves. Blanch for 30 seconds, then refresh under cold water. Strain, squeeze out the excess water, set aside to dry, then coarsely chop.
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4
Place 1 tablespoon of the oil and the butter in a medium saucepan over medium heat. Add the shallots and saute for 4 to 5 minutes, stirring once or twice, until soft but not colored. Add the garlic and leek and cook for another 2 to 3 minutes. Add the potatoes and cook for 5 to 6 minutes, stirring frequently, until shiny and glossy.
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5
Pour over the chicken stock and bring to a boil over medium-high heat, then simmer for 8 to 10 minutes, until cooked by still retaining a bite. Add the blanched parsley and arugula and cook for a final minute, then remove from the heat and add the spinach, along with 1 1/2 teaspoons of salt and a good grind of black pepper. Transfer to a blender, blitz well until completely smooth, and set aside until ready to use.
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6
Preheat the broiler to 400u00b0 F or to its highest setting. Spread the halibut fillets out on a large parchment-lined baking pan and brush them with the remaining 2 tablespoons of oil. Season with 1 1/2 teaspoons of salt in total and a good grind of black pepper and cook for 6 to 7 minutes, until the halibut is almost cooked. Remove the baking pan from under the broiler and lay a rectangle of nut butter on top of each fillet. Return to the broiler and cook for a final 2 to 3 minutes, until the crust is golden brown. Remove from the oven and squeeze over the lemon juice.
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7
Warm the vichyssoise and spoon it into shallow wide bowls. Lay a halibut fillet on top, place the radish pieces alongside, and serve at once.
