In a large deep skillet, heat the butter over medium-low heat.  Add in the onion, potato, celery, and carrots. Sauté until onions are translucent and the potatoes and carrots are a little softer, 10 to 15 minutes. Stir in the mushrooms and sauté for a few more minutes.

Next, add in the flour and stir until all of the vegetables are nicely coated. If your pan is too dry then add a little more butter or oil. Continue to stir for a few more minutes and then slowly stir in the broth.

Slowly add in the milk and stir until there’s a nice thick consistency, but if it gets too thick then add a little more milk or veggie broth. This sauce should be really creamy because the pastry will absorb some of that sauce and you don't want your pot pie to be too dry. Season with salt and pepper to taste, then stir in the frozen peas and fresh herbs. Pour veggie sauce into a 9x9 baking dish or round dish.

Preheat the oven to 400 degrees.

For the puff pastry, lightly dust a clean surface with a little flour and then run a rolling pin over the dough just a couple of times to thin it out a bit. For this step, I typically cover the small area that I’m working on on my kitchen counter with a few sheets of plastic wrap and then sprinkle it with flour. Once done, simply discard the plastic wrap. This makes the clean up process much easier.

Use a biscuit cutter to make as many circles as possible. Then starting from the center, carefully place them on top until completely covered.

For the simplified version, simply place the pastry sheet over your baking dish of vegetables, trim any excess off with a knife, and then neatly tuck the sides inside of the pan.  Cut a few slits on the top of dough with a knife.

If using egg wash, in a small bowl, whisk the egg and milk together and brush the egg wash mixture over the top of dough evenly.

Place the pan on a baking sheet just in case some of the liquid bubbles over. Bake on the center rack for 25 to 35 minutes or until the top is golden brown and the sauce is bubbling.

Once your pie is done, let cool slightly and serve and enjoy!