Preheat the oven to 350°F and grease a 9x9-inch casserole dish.
Heat the butter and olive oil in a large skillet over medium-high heat.
Add the chopped onion and sauté for 2 to 3 minutes until it begins to soften.
Stir in the mushrooms and cook for 1 more minute.
Add the minced garlic and sauté for an additional 30 seconds.
Whisk in the Italian seasoning, chicken broth, and heavy cream. Let the mixture cook until it begins to thicken.
Add in the mozzarella and parmesan, whisking until the sauce is thick and creamy.
Stir in the shredded chicken and drained palmini noodles. Cook just until the mixture is slightly reduced and most of the liquid is absorbed.
Transfer everything to the prepared casserole dish.
Bake for 30 minutes, or until the top is golden and the sauce is bubbling.