You will also need a grill pan lined with foil with a grill rack on top.

1. First of all, don't peel the onions: simply trim off the root and top before cutting each one across into four slices about ¾ inch (2 cm) thick. Keeping the slices whole, transfer them to the grill rack (you might have to do this in two batches, depending on the size of your grill), then brush them with oil and season with salt and freshly milled pepper. Now position the grill pan so that the onion slices are about 4 inches (10 cm) from the heat and grill for 7 or 8 minutes until the onions are browned – indeed within a whisker of being blackened.
2. While that's happening, prepare the Parmesan by shaving it into wafer-thin pieces with a potato peeler. For the onions the next stage needs a little care: use a palette knife to turn the slices over so that they don't break up into their constituent rings. Repeat the same oiling, seasoning and grilling on the other side, then remove from the heat and leave them on one side until they're cool enough to handle.
3. Now discard the outside layers and any parts of the onion slices that are too blackened or chewy to eat, and separate the cold onion into rings. Put about a quarter of the rings in a layer on a serving dish and gradually build up the salad, intermingling onion rings with the torn rocket leaves and shavings of Parmesan, sprinkling with more salt and pepper, lemon juice and about 3 tablespoons of olive oil as you go. This salad should not be tossed, so it relies on the cook to mingle the ingredients as the salad is put together. Serve at room temperature.