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Prepare a charcoal or gas grill for direct, medium-high heat (the charcoal or gas flame is directly under the cooking area, and you can hold your hand just above grill level only 3 to 4 seconds).
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While grill heats, peel onions and cut crosswise into 1/3-in.-thick slices.
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In a large bowl, stir together 1 1/2 tablespoons oil, vinegar, brown sugar, salt, and pepper. Add onion slices and mix well to coat.
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If cooking over charcoal, use a grill skillet or basket; if cooking over gas, use a grill sheet or basket (lightly brush sheet with oil, or spray with cooking-oil spray). Transfer onions to grill skillet, sheet, or basket, reserving oil mixture in bowl.
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Place skillet or basket on grill (close lid if using gas) and cook, gently shaking once or twice to turn onions, until brown and limp, about 20 minutes.
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Return onions to bowl and mix to coat with reserved oil mixture. Fig. B. Serve warm or at room temperature.