Pre-heat oven to 375 degrees F. Spray six 4-inch diameter (8-ounce volume) ramekins or oven-safe small pots with nonstick spray. Place an oven rack in the middle position of the oven. Heat a large skillet over medium heat. Melt butter in the heated skillet.
Add the onion, carrots, and celery. Cook for 5 minutes, stirring periodically, or until the onion starts to turn translucent.
Add in cremini mushrooms and garlic, stirring occasionally so the garlic does not burn. Cook 5 minutes or until mushrooms are tender and any liquid they express has been absorbed my the mixture.
Stir in flour until all vegetables are coated. Carefully pour in chicken broth and heavy cream. Whisk together until combined. Simmer for 3 to 4 minutes, until thickened stirring occasionally.
Season with thyme, salt, and black pepper. Stir in cooked chicken, frozen peas, and Italian parsley.
Remove skillet from the heat and allow to cool to room temperature while you prepare the pie crust.
Cut six 4 1/2-inch circles out of the pie crust. Place these inside the ramekins to form the crust.
From the remaining pie dough cut out 4-inch long strips that are about 1/2-inches wide (these will make the top of the individual pot pies).
Fill the ramekins with the chicken mixture until it just reaches the top. Place the dough strips across the filling for a top crust and to create a mummy-like weave on top of the filling, overlapping pieces every so often. Press the ends down along the edge so they stick.
Whisk the egg in a small bowl with 1 teaspoon of water. Brush egg over top of the dough.OPTIONAL: Sprinkle on coarse sea salt on top of the egg wash for additional texture and flavor. Place ramekins onto a rimmed baking sheet or cookie sheet and into the oven. Bake 25-30 minutes, or until the dough is golden brown and the filling is thick and bubbly.
Allow pot pies to cool slightly before serving.