Preparation

• Heat a gas grill to medium high or prepare a medium- hot charcoal fire. (Be sure the grate is hot, too.) Wipe the mushrooms clean and trim off the stems. If using portabellas, scrape out the black gills with the side of a spoon. Put the clean whole mushrooms in a large bowl, drizzle with 5 tablespoons of the oil, and gently toss. Sprinkle in a pinch of kosher salt and toss again. Grill the mushrooms directly over the heat until tender and well marked, 3 to 5 minutes on each side. If using portabellas, quickly cut the grilled mushrooms into 1-inch slices.

  Portion the arugula among four plates and top with the hot mushrooms. Garnish with the nuts and cheese and a generous drizzle of olive oil. Sprinkle lightly with fleur de sel or other sea salt and a grind of white or black pepper. Serve immediately.