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Prepare the barbecue for medium-high heat.
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Whisk the oil, thyme, garlic, and chile flakes in a large bowl to mix well.
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Add the broccolini and toss to coat.
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Season to taste with salt and pepper.
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Grill the broccolini until tender and lightly charred, turning as needed - about 8 minutes.
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Transfer to a plate and serve.