Place zucchini on a vegetable spiralizer. Use the smaller holes and make spaghetti pasta.
In a large skillet over medium heat, add 1 tablespoon ghee or butter and sauté mushrooms until slightly soft, about 3 minutes. Add zucchini pasta and cook until tender, about 6-7 minutes. Place pasta in a serving dish and cover tightly.
In the same skillet over medium heat, add the remaining 2 tablespoons ghee or butter and stir to melt.
Add flour and cook for 1 minute while stirring continuously. Pour in broth and milk and stir until it reaches a gravy-like consistency. Add parsley, 1/2 cup parmesan, salt, pepper, and red pepper flakes and stir until cheese melts.
Pour gravy over zucchini pasta and toss to combine. Sprinkle with additional parmesan and fresh basil, if desired.