Preparation

• Heat the grill. Remove any wilted or brown-tinged leaves from the heads of endive and halve them lengthwise. Dip them in cold water and shake lightly. Toss with olive oil and sprinkle with salt.
• Grill the endive on only the cut side over medium-high heat until just tender when pierced with a fork, 10 to 13 minutes. Arrange the arugula on four salad plates and set the endive halves on top. Drizzle with a little more olive oil and a squeeze of lemon; top with the shaved Parmigiano and freshly ground black pepper and serve.