Bring a large pot of generously salted water to a boil. Add the pasta and cook it according to the directions for al dente (about 12 minutes for gemelli). Reserve 1 cup of water water, then drain the pasta.

Meanwhile, heat the oil in a large skillet over medium heat. Add the garlic and cook 2-3 minutes, until softened and fragrant. Stir in the mushrooms and cook 5 minutes, until deeply browned and softened.

Over low heat, stir in the pasta and reserved cooking water. Cook 2-3 minutes, until the water is reduced. Stir in the arugula and red pepper flakes. Season to taste with salt and pepper. If desired, top with Parmesan cheese.