Melt the butter in a large dutch oven over medium heat. Add the onions and cook for 8 - 10 minutes or until they start to get translucent. Add the flour and cook for an additional 2 minutes. Add the mushrooms and continue to cook for an additional 2-3 minutes, stirring continuously so that the flour doesn't brown or stick to the bottom of the pot. Add the chicken broth to the dutch oven 1 cup at a time, allowing each cup to be absorbed before adding the next. Season with black pepper. Add the cream and milk all at once and allow the flour mixture to thicken for 5-7 minutes or until it just coats the back of a spoon. Add the diced potatoes, chicken, corn, peas and carrots along with the garlic powder, and red pepper flakes; allow the ingredients to heat through, about 3 minutes. Check for seasonings, add salt and pepper as desired.

Position a rack in the center of the oven and preheat the oven to 385 degrees F (or as directed by the packaging of your puff pastry sheets). Turn the ramekins or the baking pan upside down on the puff pastry sheet and cut out a circle that's slightly larger than the rim of the baking pan or ramekin. Alternately, you can cut strips and use them to make a lattice on top of the filled ramekins. Place the chicken pot pie mixture into 6 large ramekins or a large enough baking pan to hold all the mixture. Top with the cut out puff pastry sheets. Beat the egg and water together, brush the tops of the puff pastry with the egg mixture. Cut a slit in the center if you're using a circular cut out for the puff pastry crust.

Place the ramekins or baking pan on a baking sheet and bake for 25-30 minutes or until the puff pastry gets lightly golden on top. Serve warm.