To the same skillet over medium-low heat, add the butter. Once melted, add the garlic and cook for 1 minute.
Add the mushrooms and cook for 6 to 7 minutes, or until they release their juices and the liquid has reduced. Stir in the apple cider vinegar, ½ cup of the chicken broth, heavy cream, salt, dry mustard, and Italian seasoning.
In a small bowl, mix the cornstarch with the remaining ½ cup chicken broth until fully combined. Add the mixture to the skillet and simmer, stirring constantly, until it thickens slightly, about 2 to 3 minutes.
Nestle the cooked chicken into the mushroom gravy.
Serve the chicken and mushroom gravy over mashed potatoes. Garnish with parsley and serve immediately.