Cut the chicken into cubes. Heat oil in a pan over medium-high heat. Add the chicken and cook for 5-6 minutes.
Add the diced potatoes and broccoli florets and cook for 4-6 minutes.
Add heavy cream, shredded parmesan cheese, cream cheese, butter, minced garlic, black pepper and salt. Stir and cook over medium heat until the ingredients are combined and the cheese is melted.
Pour into a greased 10-inch cast-iron skillet or baking dish.
Cover with a sheet of thawed puff pastry and brush with a beaten egg. Place the pan on a rimmed cooking sheet to catch spills.
Bake at 400 degrees for 25-30 minutes, until golden brown.