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1
Put chopped root vegetables in a medium pot and cover with water. Bring to a boil and add 1 tsp. salt. Cook vegetables until tender, about 15 minutes.
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2
Meanwhile, heat cream and 2 tbsp. butter in a medium saucepan over low heat. In a small bowl, combine tomato, 1 tbsp. olive oil, the vinegar, and salt and pepper to taste. Set tomato sauce aside.
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3
Drain root vegetables. Return to pot, add heated cream, and mash until smooth. Season with salt and pepper, then set aside, covered, to keep warm.
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4
Slice lemons in half crosswise, pop out any seeds, and brush cut sides with vegetable oil. Heat a large frying pan (not nonstick) over medium-high heat. Char lemons by setting them cut side down in pan until browned, 2 to 3 minutes. Remove from pan and set aside.
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5
Add remaining 1 tbsp. olive oil, the shallot, and garlic to pan and cook, stirring, until sizzling, about 1 minute. Add greens, cover, and cook, stirring occasionally, until wilted and soft, about 5 minutes. Add 1 tbsp. butter and 1 tbsp. lemon juice. Cook, stirring, until butter melts. Season with salt and pepper. Keep warm, covered.
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6
Preheat broiler with rack about 4 in. from heat. In a small frying pan over medium-high heat, melt remaining 4 tbsp. butter. Use a bit of it to butter a large baking sheet.
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7
Open up ruby red trout like a book. If using rainbow trout, cut each into 2 fillets. Pat fish dry with paper towels, then lay skin side down on baking sheet. Drizzle 2 tsp. melted butter over each fish (1 tsp. per fillet), and sprinkle with salt and pepper. Broil until fish is cooked through and flakes easily, 5 to 10 minutes.
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8
Meanwhile, cook remaining melted butter over medium heat, swirling pan or stirring frequently, until butter browns, about 3 minutes. Swirl in remaining 1 tbsp. lemon juice.
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9
Divide greens and root mash among dinner plates. Arrange 1 trout (or, if using rainbow trout, 1 fillet) on each plate. Drizzle with browned butter and tomato sauce. To each plate, add a charred lemon half and some herbs or microgreens if you like.
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10
*Ruby red trout are farm-raised, as are most rainbow trout, and fed a diet of small shrimp or crab so that their flesh is rosy, like salmon. They tend to be smaller than rainbow trout.