How to Make It
In a small bowl, combine the shallot with the vinegar and season with salt and pepper. Let stand for 10 minutes, then whisk in 1/4 cup plus 2 tablespoons of the olive oil.
Meanwhile, in a large skillet, heat the remaining 2 tablespoons of olive oil. Add the mushrooms and thyme sprigs and season with salt and pepper. Cook over moderately high heat, stirring occasionally, until the mushrooms are golden and tender, about 8 minutes. Discard the thyme sprigs. Remove the skillet from the heat, add the dressing and toss to coat.
In a large bowl, combine the endive, radicchio, escarole and parsley. Using a slotted spoon, add the mushrooms. Drizzle with some of the dressing from the skillet, season with salt and pepper and toss. Add the shaved cheese and gently toss. Serve right away, passing any remaining dressing at the table.