Preheat oven to 400 °.
If puff pastry is frozen, take it out of the freezer to thaw while you prep the other ingredients.
Prep all the vegetables. Peel the carrots. Slice the carrots, celery, and asparagus. Make sure that the leeks are rinsed to remove any dirt in between the leaves before slicing. Mince the garlic and the parsley. Strip the thyme leaves from the stalks.
Peel and dice 4 small Yukon gold potatoes.
Over medium heat, add 2 tablespoons of olive oil to a skillet. Add the potatoes to the pan. Move the potatoes around the pan frequently. They will start to stick to the bottom of the pan. Use a metal spatula to release the potatoes from the pan. It is okay is there is some fond developing from the potatoes as this will help to thicken the sauce. Just don't let them brown too much. Saute for 8-9 minutes.
Add the celery and carrots to the pan along with 1 teaspoon of olive oil, ½ teaspoon of salt, and ¼ teaspoon of black pepper. As the vegetables are sauteed, they will release some water. Scrap the fond off the bottom of the pan. Saute for 5 minutes.
Add the leeks, asparagus, and minced garlic to the pan. Saute for 6 minutes. The vegetables are being sweated at this point. They should only cook until they are crisp-tender as they will continue to cook while the pot pies baking.
Once the vegetables are done cooking, remove them from the pan onto a plate. Try to spread them out to cool.
Add 2 tablespoons of olive oil to the pan. Once the oil is hot, add the diced chicken and season with ½ teaspoon of salt and ¼ teaspoon of black pepper. Raise the heat to medium-high. Saute for 8-10 minutes. The chicken may get slightly brown on the surface. If it is not completely cooked through, don't worry. It is being baked soon.
Add the vegetables back to the pan with the chicken, gently stirring to combine. Add 2 tablespoons of unsalted butter to the pan.
Once the butter is melted, sprinkle 2 tablespoons of flour over the chicken and vegetables. Stir to coat all the ingredients. Stir constantly for 3 minutes to cook the raw taste out of the flour.
Add 2 cups of chicken stock to the pan. I add it ¼ cup at a time, adding more as the sauce starts to thicken.
Let the chicken stock get warm and start to thicken. Add the heavy cream, stirring to combine with the stock.
Once the sauce is thick, add the lemon zest and juice, chopped parsley, and the fresh thyme leaves.
Check the seasoning of the sauce. Add more salt and pepper if needed.
Fill the pie dishes with the pot pie filling. I used 5-inch pie dishes that held 1 ½ cups of filling in each.
Lay a thawed puff pastry sheet on a lightly floured surface. Roll the sheet out into a 14-inch x 14-inch square.
Use a plate or bowl as a template to cut circles out for the top of the pie dishes. Cut the circles about ½-inch larger than the size of the pie dish.
Combine a beaten egg with 1 tablespoon of heavy cream.
Brush the edge of the pie dish with the egg wash and lay the puff pastry on top. Use egg wash to adhere the extra puff pastry overhanging to the sides of the pie dish. This will prevent it from shrinking while baking.
Cut two vents in the puff pastry and brush the top with egg wash.
Bake for 30 minutes. Let it cool for 5-10 minutes before eating. Remember it is lava.
