Start by peeling the zucchini and cutting off the ends. Slice the zucchini into thin rounds or half-moons, depending on your preference. Dice the button mushrooms and mince the garlic cloves. Set aside.
In a large pot, bring salted water to a boil. Add your choice of pasta and cook according to package instructions until al dente. Drain and set aside.
In a large skillet, heat the ghee over medium heat. Once melted, add the diced mushrooms and sauté for about 5 minutes until they start to brown. Then, add the sliced zucchini and minced garlic, cooking for another 3-4 minutes until the zucchini is tender.
Sprinkle the flour over the sautéed vegetables and stir well to combine. Gradually whisk in the chicken broth and milk, stirring constantly to avoid lumps. Continue to cook for about 5 minutes, or until the sauce thickens.
Stir in the freshly grated parmesan cheese, kosher salt, black pepper, and crushed red pepper flakes. Mix until the cheese is melted and the sauce is creamy.
Add the cooked pasta to the skillet and toss everything together until the pasta is fully coated in the cheesy mushroom and zucchini sauce. If the mixture seems too thick, you can add a splash more chicken broth or milk to reach your desired consistency.
Remove the skillet from heat and fold in the chopped flat-leaf parsley. Serve the Cheesy Mushroom & Zucchini Pasta hot, garnished with fresh basil if desired.