Heat the stock and ladle 2 cups into a medium bowl. Add dried mushrooms and let soak for 20 minutes, then drain, reserving the liquid. Pour liquid through a fine sieve lined with cheesecloth or paper towels to catch any grit. Add mushroom liquid back to warm stock. Keep stock heated over medium heat. Pat soaked mushrooms dry and saute in a large skillet with 1 tablespoon olive oil.
Heat remaining olive oil in a large, heavy saucepan over medium heat. Add shallots and cook until softened. Add rice and cook, stirring, until the rice becomes translucent, about 3 to 5 minutes. Add vermouth and stir until absorbed by rice. Add warm mushroom stock to rice, 1 cup at a time, stirring constantly. All stock must be fully absorbed before the next cup of stock is added. After about 20 minutes, the rice should be tender but not mushy, it should have a creamy texture. Add more stock if needed. Fold in Sauteed mushrooms, Parmesan, and season with salt and pepper. Let stand for a minute before serving. Sprinkle with Parmesan, if desired.