Grease a large square or rectangular baking dish. (or 6 small baking dishes if you are making individual pot pies).
Melt the butter in a large, tall saucepan. Add flour and whisk to ensure there are no lumps, then add the chicken stock. Cook out this mixture for 3-5 minutes while continuously stirring. Check the consistency by dipping the back of a spoon into the sauce and running your finger along the back of spoon. You want the sauce to cling to the spoon and not run over the swipe you made. Season with the salt, pepper, and cayenne (if using). (Taste the sauce and see if your sauce needs more seasoning).
Next, add the cream and stir to combine. Then, add the potatoes, carrots, onion, and garlic to the sauce. Cook the vegetables in the sauce for 15 minutes until tender and you can pierce with a fork, but not falling apart. (The mixture will be quite thick, but if too thick or not almost covering the vegetables, add a touch more stock, remembering that the vegetables will also release a bit of liquid, so do not add much). Once vegetables are tender, add chicken and frozen peas, and simmer for 2 minutes. Transfer the filling into a clean bowl and chill for one hour, or until cool.
Preheat the oven to 400˚F / 200 ˚C.
Roll out the puff pastry, using a bit of extra flour to ensure the pastry doesn’t stick to your work surface. Roll it out an inch larger on the borders in the shape of the dish(es) you are cooking your pot pie in.
Carefully spoon your chilled filling into your dish(es).
Break the egg in a small dish and add a tablespoon of water or cream. Whisk with a fork and brush this egg wash on the edges and rim of your dish. Lay your pastry over the top, being careful not to stretch the pastry. Seal the edges of the pastry by lightly pushing it onto the rim of your dish to make sure it is secure. Brush the top and sides of the puff pastry with more egg wash. Use a knife to cut three small slits on top for air escape.
Place your large pot pie dish in the oven (or your individual pot pies on a large baking sheet then in the oven), and bake for 25-35 minutes. Bake until your pastry is a nice golden, dark brown and there are no more grayish raw patches. Let cool for 5 minutes before serving.
Enjoy!