Heat oil over medium-high in a Dutch oven pot or large skillet with a lid. Add in mushrooms and garlic and cook for about 2 minutes. Season with salt and pepper.
Raise heat to high; add in white wine and allow to reduce by half. Pour in broth; bring to a boil.
Mix in chicken, sun dried tomatoes, and lemon zest. Season with the red pepper flakes and a few grinds of salt and black pepper, to taste.
Add in cream and warm through. Stir in the mozzarella, Parmesan, and parsley.
This recipe calls for thin spaghetti, which is in between regular and angel hair. Make sure that’s what you use, or the cooking time and amount of broth will need to be adjusted.