- 1/2 cup Champagne vinegar
- 2 teaspoons sugar
- 1 1/2 teaspoons salt
- 1 teaspoon black pepper
- 1/2 cup finely chopped shallots (4 small)
- 1 cup extra-virgin olive oil
- 1/2 pound whole fresh portabella mushrooms, stems discarded
- 1/2 pound fresh shiitake mushrooms, stems discarded
- 1/2 pound fresh cremini mushrooms, trimmed
- 3/4 pound fresh chanterelle mushrooms, trimmed
- 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)
- 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.