Heat olive oil in a large skillet over medium heat. Season chicken with salt and pepper, then sauté until golden and cooked through. Remove and set aside.
In the same skillet, cook mushrooms until softened and browned. Remove and set aside with the chicken.
Add butter and garlic to the skillet, cooking until fragrant. Stir in heavy cream and bring to a simmer.
Gradually whisk in Parmesan until the sauce is smooth and creamy.
Cook pasta according to package instructions. Drain, reserving 1/2 cup of pasta water.
Combine the pasta, chicken, and mushrooms in the sauce. Adjust consistency with reserved pasta water if needed.
Garnish with parsley and serve immediately.