Preheat the oven to 400 degrees F. In a large skillet, heat the olive oil over medium-high heat. Add the sugar snap peas and cook, stirring frequently, until they are tender, about 5 minutes. Stir in the parmesan cheese and salt and pepper to taste. Cook and stir until the cheese is melted and the mixture thickens, 2 to 3 minutes more. Remove the skillet from the heat and add the mushrooms. Toss to coat.