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Preheat broiler.
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Stir together 1 1/2 tablespoons oil, garlic, oregano, cinnamon, allspice, 3/4 teaspoon salt, and 1/2 teaspoon pepper. Rub spice mixture all over chops, then broil on a broiler pan 2 to 3 inches from heat, turning once, 6 to 7 minutes total for medium-rare.
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Meanwhile, heat remaining tablespoon oil in a 5- to 6-quart heavy pot over medium heat until it shimmers, then cook spinach, stirring, until wilted and tender, 3 to 4 minutes. Transfer to a colander and press gently to remove excess water. Return spinach to pot and add yogurt, dill, and lemon juice, then heat over low heat, stirring, until yogurt is just warmed through (do not let boil). Season with salt and pepper.
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Serve chops with spinach.