Preheat oven to 190 degrees Celsius (375 F).
Make the Chicken and Vegetable Mixture-part 1: In a medium pot, cook onions, potatoes, celery and carrots in a little of olive oil until the potatoes and carrots are fork tender (about 5-7 minutes) Add garlic and season with salt and pepper. Remove the vegetables out of the pot and keep warm.
Make the Chicken and Vegetable Mixture-part 2 Add a little more olive oil in the pan and add chicken sauté until the chicken is no longer pink. Salt and pepper to taste, add paprika and herbs de Provence. Add white wine to deglaze the pan. Add the vegetables back to the chicken and turn the burner down to low or off while you make the roux.
Make the Chicken Gravy: Place equal amounts of butter and flour into a sauce pan. Stir continuously and allow the flour taste to cook off about 2 minutes. Slowly add milk a little bit at a time while writing the roux with a whisk. Stir and add milk until it is the consistency of a creamy soup. Season with salt and pepper, paprika, herbs de Provence and nutmeg to taste. Add the roux mixture to the chicken and vegetable mixture and stir until well incorporated. Turn the burner off and keep chicken mixture warm.
Make the Pie Crust: If you have a food processor, this step is a breeze. Place your very cold butter, salt and flour in the processor and pulse until it it makes little granules. (If you have a small food processor like I do, you might have to make the crust in 2 batches as it will not all fit into the mini food processors) Add your super cold water to the food processor and pulse until the dough comes together and forms a ball. Depending on your humidity level, you may need a little less or a little water so just add a little bit at a time and stop once your dough forms a ball. If you do not have a food processor you will have to do this step by hand. (There is no need to let the dough rest, you can begin working with it right away. This dough is really easy to work with.)
Assembly- Cut the dough into 8 sections (if making 4 mini chicken pot pies- I used 4 mini cheesecake tins and these worked brilliantly or your could use medium ramikens) or 2 sections (if making one large chicken pot pie). Place a little flour on your clean and dry surface and roll out the dough in a round disks to fit the size of your pie tins with about a 1 inch overlap. Spray your pie tins with a little cooking spray and place the bottom crust flat on the bottom of pie plate and allow 1 inch to hang over the edges.
Put the chicken,vegetable and gravy mixture on top of the bottom crust of your pie plates/plate. If you have mini pie plates, divide the chicken, vegetable and gravy mixture evenly amongst the 4 pie tins. If using just one large pie plate, place all the chicken, vegetable and gravy mixture inside the one pie plate. Cover the chicken pot pies with top crust and pinch edges over and use a curved edge or even just use a fork to pinch edges close for a simple design. Next, make vent holes with a knife or even a cute little heart on top to allow the steam to escape. Bush tops of mini chicken pot pies with beaten egg. Bake in oven for about 1 hour. The crust should be golden brown and the chicken gravy should be bubbling.
Allow mini chicken pot pies to cool for 5-10 minutes, if you can wait that long. Remove the mini chicken pot pies from the cheesecake tins (if using cheesecake tins) Serve hot with a nice tossed salad. Enjoy!