- 2 teaspoons unsalted butter
- 8 ounces fresh shiitake mushrooms, stems discarded and caps finely chopped
- 2 shallots, minced
- 1/4 cup water
- 1 1/2 tablespoons finely chopped fresh tarragon
- 2 whole large eggs
- 6 large egg whites
- 1/4 cup finely shredded Parmesan
- 1/2 teaspoon kosher salt
- 8 thin slices prosciutto
- 24 thin fresh chives
- Melt butter in a 9- to 10-inch nonstick skillet over moderate heat, then cook mushrooms and shallots, stirring occasionally, 3 minutes. Add water and cook, stirring, until liquid is evaporated and mushrooms are tender and golden, about 5 minutes. Stir in tarragon.
- While mushrooms are cooking, lightly beat together whole eggs, whites, parmesan, kosher salt, and pepper to taste.
- Preheat broiler.
- Add egg mixture to mushrooms, then cook over high heat, stirring briskly, until eggs are softly scrambled, 2 to 4 minutes. Reduce heat to low and form frittata into a 6 1/2-inch square with a spatula. Cook over low heat until bottom is set, about 2 minutes.
- Place skillet under broiler (wrap nonmetal handles in foil), 5 to 6 inches from heat, and broil until eggs are just firm to the touch and barely golden, 1 to 2 minutes.
- Transfer frittata to a cutting board and cool. Trim edges of square, then cut frittata into 24 rectangles.
- Cut each prosciutto slice lengthwise into 3 strips. Wrap a prosciutto strip lengthwise around each egg rectangle, then tie a chive around crosswise. Serve at room temperature.