Preheat oven to 375 degrees F (190 degrees C).
Heat oven proof skillet. Add Olive Oil (2 tablespoon). When oil is hot, add Carrot (1), Potato (2), Sweet Potato (1), Onion (1), Celery (2 stalk), Salt (to taste), Ground Black Pepper (to taste), and Fresh Rosemary (1 teaspoon).
Cook covered, over medium-low heat, stirring occasionally, for 10 minutes.
Add Summer Squash (1) and Chicken (1 cup) and cook for about 3-5 minutes more, or until vegetables are tender.
Add Garlic (2 clove) and cook for 1 minute more.
Whisk Chicken Stock (1 1/2 cup) or pan drippings with All-Purpose Flour (2 tablespoon) and Water (1/2 cup).
Add to the skillet, turn the heat to high, and bring it to a boil. Let it thicken for about 2-3 minutes.
Whisk in the Milk (1/2 cup), turn heat to medium-low, and cook for 1-2 minutes, or until steam rises, but do not boil. Remove from heat, taste and adjust seasoning if needed. Set on a baking sheet.
Roll out Pie Crust (1).
Top the filling with the crust. Be careful, the skillet is hot! Make a few air vents with a sharp knife.
Brush with the Egg (1) and sprinkle with Coarse Sea Salt (to taste). Bake for 22-30 minutes, or until crust is browned and flaky.
Let cool for a bit, then serve warm.