In a large skillet over medium heat, melt butter with olive oil.
Add mushrooms and cook for 10 to 12 minutes, stirring occasionally. The mushrooms should start to turn golden brown and release their moisture.
Transfer the mushrooms to a plate and tent loosely with foil to keep warm.
In the same skillet, add garlic and cook for about 1 minute, stirring frequently to avoid burning.
Whisk in cream cheese, Parmesan cheese, and heavy cream. Continue stirring until the mixture is smooth and all the cheese has melted.
Sprinkle in Italian seasoning, kosher salt, and black pepper. Stir well to combine and let the mixture simmer for 2 to 3 minutes, allowing the flavors to come together and the sauce to thicken slightly.
Add chicken broth and whisk to combine, loosening the sauce to your desired consistency.
Add the mushrooms back into the skillet and toss gently to coat them evenly in the creamy sauce.
Remove from heat and sprinkle with fresh parsley, if using. Serve immediately.