Heat butter in a large skillet over medium heat until melted. Saute onion for two minutes, then add garlic, carrots, and celery and saute another four minutes, stirring occasionally.
Add mushrooms and diced potatoes to the pan and season with sea salt, pepper, thyme, rosemary, and parsley. Continue cooking veggies over medium heat for another 12 minutes (or until mushrooms are softened and have released their liquid), stirring occasionally.
Sprinkle flour over vegetables, stir to coat, and continue sauteing over medium heat for another two minutes.
Add in broth and bring to a boil. Stir in milk and simmer pot pie filling over medium heat, stirring frequently, for about ten minutes or until potatoes are tender and mixture is starting to thicken.
Season with a little more sea salt & black pepper to taste, then stir in mozzarella until melted and well incorporated. Stir in peas and turn off heat under the pan.
Place your pie dish on a rimmed baking sheet (in case the pot pie filling bubbles over while cooking). Pour your creamy vegetable mixture into the pie dish, then top with the pie crust, pressing it down and crimping around the edges.
Beat egg and water together in a separate small bowl, then brush pie crust with egg wash and cut a couple of slits in the top of the crust to vent.
Bake your vegetarian pot pie at 400 degrees for 30 minutes, until nicely browned. Let it sit for a few minutes before serving.
Note: This recipe requires a good bit of chopping and prep work -- it's not that it's difficult per se, but it is a little more time-consuming than many of the other recipes I post. To reduce the prep time on the day you make the pot pie, you might want to pre-shred your cheese and chop all of your veggies (except for the potatoes) the night before.
Vegetable Pot Pie with Potatoes and Mushrooms from Mashup Mom: https://www.mashupmom.com/vegetable-pot-pie-with-mushrooms-and-potatoes/