Preheat the oven to 350°F and grease a 9×13 inch casserole dish with butter. In a large pot of salted boiling water, cook pasta until just shy of al dente; reserve 1/2 cup of the cooking liquid, then drain and set the pasta aside with a loose cover.
In a large skillet over medium-high heat, heat the olive oil and sauté the mushrooms for about 3 minutes until softened. Add the chopped onion and continue cooking for 5 to 7 minutes until the onions are translucent and lightly golden. Stir in the minced garlic and cook for another minute until fragrant. Remove from heat and combine with the chicken.
In the same pot used for pasta, melt the butter and whisk in the flour, cooking for 1½ minutes until golden. Gradually whisk in the chicken broth, lemon juice, salt, and pepper until smooth. Add the half & half and bring the mixture to a simmer. Taste and adjust seasoning as needed.
Return the pasta to the pot and add the chicken mixture, parsley, and creamy sauce. Stir thoroughly to combine, incorporating some reserved pasta water if desired for extra creaminess. Spread the mixture evenly into the prepared casserole dish and top generously with shredded mozzarella.
Cover the dish with foil and bake for 20 minutes. Remove the foil and continue baking for an additional 15 minutes. For a golden top, broil for 1–2 minutes at the end.