Cut (or break) off the woody ends from the asparagus. Boil the spears in a large pan of salted water for 3 minutes. Drain, then plunge the spears into ice-cold water to stop the cooking and set the colour. Pat the asparagus dry.
Oil the spears lightly. Leave a large cast-iron griddle over a high heat until it’s very hot, then arrange the spears on it in a single layer. (You may have to griddle the asparagus in two batches.) Reduce the heat to medium and cook the spears for 3-4 minutes. Turn them with tongs and cook for a few more minutes, or until the spears are tender to the point of a knife and lightly gilded.
Transfer the asparagus to a serving platter and sprinkle on a few drops of balsamic vinegar. Serve while still hot, although the spears will also taste very good at room temperature.
To get ahead, you can prepare the asparagus to the end of step 1 and keep refrigerated for up to 24 hours.