Cook the spaghetti according to the package instructions.
Heat a skillet over medium heat, then add the olive oil and butter. Sauté the garlic until slightly browned, then add the mushrooms. Stir a few times before adding the chicken broth and whipping cream. Season with salt and cayenne pepper, then stir in the Parmesan cheese.
Transfer the spaghetti to the skillet and stir to combine well with the sauce. Add the baby spinach, and once it starts to wilt, turn off the heat. Stir in the chopped parsley and serve immediately.