Preheat your oven to 425F and grease four oven-safe ramekins with non-stick cooking spray. Heat a large high-sided skillet over medium heat.
Add the olive oil, onion, celery, and carrots and cook until the vegetables have softened and started to brown slightly-- about 5-7 minutes.
Once the vegetables have browned, add the garlic and thyme and cook for an additional minute.
Next add the butter. Once the butter has melted, add the flour and stir to combine. Cook for one minute. Then slowly add the stock and milk, stirring constantly.
Cook for 2-3 minutes or until the sauce has thickened enough to coat the back of a spoon.
Add the vegetables back to the pan along with the shredded chicken, frozen peas, and parmesan cheese (if using). Stir to combine. Season with salt and pepper to taste.
Divide the pot pie mixture between the ramekins filling each one about ½” from the top.
Cut out four circles from the puff pastry, making sure the circles are large enough to fully cover the top of the ramekins.
Place a circle of puff pastry on top of each ramekin and slit the center with a sharp knife so the air can vent.
Brush the top of the puff pastry with the beaten egg and sprinkle with flakey sea salt, if desired.
Bake for 30-35 minutes, or until the puff pastry is golden brown. Remove from the oven and allow the pot pies to cool for at least 10 minutes before serving (this will help the filling set).
Store any leftovers in an airtight container in the fridge for up to two days.