Place chicken and vegetables on sheet tray, rub chicken with salt and pepper to taste. Place in preheated 425 degree oven for about 30 minutes or until the skin turns golden brown.
Place the chicken and vegetables that were roasted into a stock pot. Add in the bay leaves and box of stock. Add water until the chicken is just covered. Let simmer on stove top for 2 hours.
When stock is done cooking, take out the chicken with tongs and let sit until cooled. While chicken is cooling, strain the liquid into a bowl with a fine mesh colander. You can discard the strained items.
When chicken is cool to the touch, throw away the skin and bones, cut chicken into medium sized cubes and place int he fridge with the stock until ready to assemble the filling.
For the Crust:
You can make the crust while the stock is cooking to save time later. Place the flour and salt in a bowl and mix. Add in the cream cheese and butter and with your hands start to form a dough. You can do so by squishing the butter and cream cheese through your fingers and incorporating the flour. Keep doing this over and over until you have a crumbly dough.
Put mixture onto clean counter top and continue to manipulate the dough. This may take a while but you want it to resemble a dry dough form. Shape it into a disk and wrap with plastic wrap, place it in the fridge until ready to assemble pot pie.
For the Filling:
In a large skillet, let the butter melt over medium low heat, add in the carrots and cook until tender. Add in the green beans and heat through. Make a well in the bottom of the skillet and sautee the garlic until fragrant and mix with the carrots and green beans. Add in the cubed chicken. Sprinkle with the flour and mix together. Let cook for one minute.
Add in the stock and let thicken, stir occasionally. Add in the dried spices and stir to combine. Add in the cream cheese in small pieces and let melt, don't worry if they don't melt all the way, it will be super yummy! Taste and add salt and pepper if needed.
Let thicken for a couple more minutes and if it is too thick, add in a splash more of chicken stock. If it is too thin to your taste, add in a little cornstarch slurry (equal parts cornstarch and water whisked together).
Just before you are ready to put the filling in the baking dish, add in the frozen peas and stir them in. Place mixture into preferred baking dish or pie dish.
Roll out the crust on a floured surface into about 1/4 of an inch thick. Place on top of pie dish. Whisk the egg with a splash of water and brush it on the crust. You will have excess egg.
Cut a few vent holes in the crust, place on a sheet tray (do this or you will probably have a pot pie mess in the bottom of your oven!) and pop it into a preheated 375 degree oven.
Cook for 25-35 minutes until the crust is golden brown and the filling is bubbling. If you are nervous about the crust get too brown too fast, you can place a piece of foil loosely on top for the first 15 minutes of cooking, then take it off for the remaining time. If you don't see your crust browning enough, after 35 minutes of cooking put on the broiler and watch extremely closely until the color you want is achieved.