Make sure you let the puff pasty thaw for 40 minutes before you use it.
In your crock pot, add your carrots, celery, and onion. Salt and pepper your chicken, on both sides, then place the chicken on top of the vegetables. Now pour in the wine and chicken broth. Finally, add the fresh or dried thyme. Set your crock pot on either low (for 4-6 hours) or high (for 3-4 hours).
After 3 hours, check to see if your chicken is finished cooking, if it's a little pink, don't worry, you'll be finishing the cooking in the oven. Put the chicken on a plate and shred when it's cool enough to handle. Once the veggies are tender, stir in the frozen peas, and turn the crock pot off.
Preheat your oven to 375 degrees
In a large pan, melt 4 tablespoons of butter over medium-high heat. Once the butter is completely melted, add the flour, and slowly whisk until the flour and butter are incorporated. Cook the flour and butter for a couple of minutes, constantly stirring. Continue whisking as you slowly add the heavy cream into the pan. Once the cream is fully incorporated, slowly add, a ladle at a time, vegetables and broth from your slow cooker, into the flour, whisking after each addition, to prevent lumps. Keep ladling and whisking the ingredients together until everything is well combined. Turn up the heat a little bit, and cook the pot pie filling for a few minutes. Try not to bring the contents to a rapid boil, but you want to heat the mixture well enough so it starts to thicken. If you like you're pot pie filling thicker, continue cooking until you reach the thickness you desire. You can always add a splash of chicken broth to thin out the filling, if it gets too thick.
Once you get the filling to your liking, add back the shredded chicken, parsley, and taste for additional salt and pepper. Turn off the heat and set aside while you prepare your ramekins.
Place 4 ramekins on a tin foil lined cooke sheet. Spray each ramekin with a little cooking spray. Spoon the pot pie mixture, evenly into all 4 bowls.
Roll out your thawed puff pastry. Cut the pastry into 4 circles, big enough to cover each ramekin (see notes). Carefully cover each ramekin with the puff pastry, and pinch the pastry into the sides of the ramekins, so it stays put.
Using a an egg wash, brush the egg on top of each pastry, then pop the ramekins into the oven for approx 12-20 minutes, or until the pastry is a nice golden brown.
When the pastry is finished baking, pull the ramekins from the oven, and allow to cool for 10 minutes before digging in.