Preheat oven to 450 degrees. Wipe mushrooms clean with a paper towel. Cut into 1/2 inch thick slices. Trim ends of beans and cut into bite-sized pieces.
Put cut beans and mushrooms into a gallon size re-sealable bag or plastic bowl. Whisk together olive oil and balsamic vinegar, pour over vegetables. Mix in bag or stir, so all the beans and mushrooms are lightly coated with the mixture.
Arrange on large cookie sheet, spreading them out well so beans and mushrooms are not crowded. Roast 20-30 minutes. Cook until beans are tender-crisp and mushrooms are cooked through. Season beans to taste with salt and fresh ground pepper, then sprinkle with finely grated parmesan. Serve hot.