Thin ribbons of Parmigiano-Reggiano carry the mushrooms' meaty robustness through each bite of greens. It might look like a lot of mushrooms when you're putting the salad together, but it allows everyone to have a generous helping.
1/2 pound baby arugula, or regular arugula torn into bite-size pieces (16 cups)
2/3 cup Parmigiano-Reggiano shavings (made with a vegetable peeler from a 2-oz piece)
Special equipment: a well-seasoned large (2-burner) ridged grill pan (preferably cast-iron)
Directions
Whisk together vinegar, sugar, salt, pepper, and shallots in a large bowl. Add oil in a slow stream, whisking constantly until combined. Reserve half of vinaigrette in another large bowl and add mushrooms to remaining vinaigrette. Toss to coat and marinate 5 minutes.
Transfer mushrooms to another bowl with a slotted spoon, discarding marinade.
Heat lightly oiled grill pan over moderately high heat until hot but not smoking, then grill mushrooms in 3 batches, turning frequently, until golden brown, about 5 minutes per batch. Transfer as grilled to a cutting board and cool to room temperature.
Cut portabellas into 1/2-inch-wide wedges, then halve shiitake and cremini mushrooms and cut chanterelles (if large) lengthwise into 1/2-inch pieces.
Transfer mushrooms to reserved vinaigrette, tossing to coat, then add arugula, cheese, and salt and pepper to taste and toss again.
