Preheat the grill to medium flame (or about 400). Toss the asparagus and broccolini in a bowl with the oil, plus ½ teaspoon salt and ½ teaspoon pepper.
When the grill is ready, arrange the vegetables on one side of the grill, crosswise over the grates, piling them slightly. Cover and cook for 5 minutes, until lightly charred underneath. Carefully turn the vegetables with a spatula, flipping them over, away from you; cover and cook until crisp-tender, about 5 minutes more.
Serve the asparagus and broccolini hot, at room temperature or chilled.
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