Preheat an oven to 375 degrees Fahrenheit
Remove the stems from the mushrooms. If needed, wash in cool water and pat dry. Heat 2 tablespoons of the olive oil in a heavy ovenproof skillet. Add the mushrooms and saute for 5 minutes turning the mushrooms once. Place the skillet in the preheated oven; roast the mushrooms for approximately 15 minutes. While the mushrooms are roasting make the vinaigrette (this can be done ahead): In a small bowl combine the remaining olive oil, Dijon mustard, salt, pepper, garlic and shallot. Whisk together and set aside. Remove the mushrooms from the oven and slice them into 1/2 inch slices. Fan the mushrooms across two warm serving plates and drizzle with some of the vinaigrette. Using vegetable peeler, peel thin, curled slices of the Asiago cheese and arrange across the mushrooms.