Melt 2 tablespoons butter in a medium skillet over medium-high heat. Add the mushrooms and saute until golden brown, about 5 minutes. Add cognac, bring to a boil, and reduce the liquid by half, 3 to 4 minutes. Lower the heat to medium, add cream and simmer 5 minutes. Remove the skillet from the heat and set aside. Bring the stock to a simmer in a medium saucepan over medium heat.
Meanwhile, heat the remaining 2 tablespoons butter with the oil in a deep, heavy medium saucepan over medium heat. Add shallots and cook until soft, about 2 minutes. Add the rice and stir to coat with the butter and oil. Add simmering stock, 1/2 cup at a time, stirring constantly with a wooden spoon. Wait until liquid is almost completely absorbed before adding more. This process will take about 20 minutes. The rice should be just cooked and slightly chewy.
Stir in the mushroom mixture and cheese. Season, to taste, with salt and pepper and serve garnished with parsley.