1. Cook the pasta according to the package directions.
2. While the pasta is cooking, heat the oil in a large skillet over medium heat. Add the shallots, garlic, and mushrooms. Saute the vegetables until tender (4-5 minutes).
3. Add the chard, reduce heat and cover for about 3 minutes. Stir, cover, and cook until completely wilted (2-3 minutes).
4. Drain the pasta, reserving 1/4 cup of the pasta water. Return the drained pasta to the pot. Add the chard mixture and the reserved pasta water. Toss to mix evenly.
5. Top each serving with Parmesan cheese and pepper. Serve immediately.