Step 1

Slice the broccoli heads lengthwise into halves or quarters, depending on size, then into spears with stems about ½ inch thick. In a large microwave-safe bowl, mix ½ teaspoon salt in ¼ cup water. Add the broccoli and toss; cover and microwave on high for 2 minutes. Toss, cover and microwave until bright green and just shy of tender-crisp, another 2 minutes. Remove from the bowl. Discard the water, wipe out the bowl and reserve it. (The broccoli can be cooled and refrigerated for 1 day.)

Step 2

In a small bowl, mix ½ teaspoon salt with the vinegar and 2 tablespoons water. Stir in the shallots and raisins. Set aside, tossing occasionally, until needed. In the reserved large bowl, whisk together the oil, harissa, lime juice, honey and ½ teaspoon each salt and pepper. Measure out ¼ cup and set aside. Add the broccoli to the bowl with the remaining dressing and toss until coated.

Step 3

Prepare a charcoal or gas grill. For a charcoal grill, spread a large chimney of hot coals evenly over one side of the grill bed; open the bottom grill vents and the lid vent. Heat the grill, covered, for 5 minutes, then clean and oil the cooking grate. For a gas grill, turn all burners to high and heat, covered, for 10 to 15 minutes, then clean and oil the grate.

Step 4

Place the broccoli on the grill (on the hot side, if using charcoal); reserve the bowl. Cook, occasionally turning the broccoli, until well charred and tender-crisp, 6 to 8 minutes. Return the broccoli to the bowl. Immediately add the reserved dressing (while the broccoli is hot) and toss. Taste and season with salt and pepper.

Step 5

Transfer the broccoli to a platter. Using a slotted spoon, lift the pickled shallots and raisins out of their liquid and scatter over the broccoli; discard the liquid. Sprinkle with the dill.