Preheat the oven to 375 degrees Fahrenheit.
Cut the mushrooms into ½ inch thick slices. Combine the mushrooms, wine, one-half of the olive oil, thyme, ¼ teaspoon salt and pepper in a roasting pan.
The pan should be just large enough to hold the mushrooms in a single layer.
Roast for about 35 minutes.
Combine the shallots, vinegars, and ¼ teaspoon of salt in a small bowl and allow it to sit at room temperature for about a half hour. Whisk in the remaining oil gradually, until thoroughly combined with the other ingredients.
Remove the roasting pan from the oven and pour off the cooking juices into a medium sized sauté pan. Return the pan to the oven and roast the mushrooms uncovered for about 10 minutes. The edges should begin to crisp.
Simmer the cooking juices from the roasting pan over medium heat until they're reduced to a syrupy, glazed consistency. Remove and discard the thyme sprigs.
Combine the mixed greens with the dressing in a large bowl and toss until the greens are evenly coated.
Serve on salad plates and top with roasted mushrooms.
Drizzle the reduced cooking juices over the mushrooms and greens. Garnish with Parmesan