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1
In a medium bowl, toss the parsley with the chopped tarragon and lemon zest. Rub the herbs all over the halibut; cover and refrigerate for 2 hours.
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2
In a large saucepan, cover the potatoes with water and bring to a boil. Salt generously and simmer over moderately high heat until tender, about 10 minutes. Drain and let cool to room temperature.
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3
Light a grill. In a large nonstick skillet, heat the 1/4 cup of olive oil. Add the garlic and shallots and cook over moderately high heat until golden, about 2 minutes. Add the potatoes and cook over low heat, smashing them gently with a spatula, until they start to break apart. Continue cooking, stirring a few times, until the potatoes are browned and crisp, about 5 minutes total. Season with salt and pepper.
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4
In a medium skillet, melt the butter. Add the whole tarragon leaves and cook over moderate heat until the tarragon is fragrant, about 2 minutes. Add the tomatoes and cook over low heat, stirring occasionally, until the tomatoes burst and the butter is browned, about 7 minutes. Season with salt and pepper.
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5
Drizzle the halibut with olive oil and season with salt and pepper. Grill the fillets over moderately high heat until nicely charred and just cooked, about 3 minutes per side. Transfer the fish to plates and spoon the tomato butter on top. Serve immediately with the smashed potatoes.
