Creamy Mushroom Gnocchi

Cook gnocchi. Simmer a large pot of salted water and cook 16 ounces gnocchi until it floats, about 2 minutes. Remove and drain. Set aside.
Saute mushrooms. Meanwhile heat 1 Tablespoon butter and 1 Tablespoon olive oil in a nonstick skillet over medium-high heat and add 8 ounces sliced mushrooms and 1 shallots. Cook, stirring frequently, until mushrooms are soft and almost all the liquid is gone. Add 2 ounces beech mushrooms (if using) and salt. Cook 3 minutes more just to heat beech mushrooms through. Transfer mixture to a bowl or plate and place skillet over heat again.
Creamy sauce. Add the remaining 2 Tablespoons olive oil and the cooked gnocchi. Move gnocchi around to cover bottom of skillet and let cook, without stirring, about 2 minutes to brown. Add 1 cup broth, 3 Tablespoons cream and 1/4 cup Parmesan and stir to move gnocchi from the bottom of the pan. Let mixture simmer until sauce is slightly thickened, about 1 minute.
Assemble. Add mushrooms back to skillet and stir to combine. Serve gnocchi immediately with a sprinkling of 1 cup arugula and red pepper flakes if desired. Season to taste with extra salt and pepper.