Preheat oven to 425ºF with rack in upper third. Heat oil in a 10-inch cast iron or other heavy ovenproof skillet over medium heat. Add onions; cook, stirring occasionally, until lightly golden, 4 to 6 minutes.
Reduce heat to medium-low. Add garlic, oregano and thyme. Cook, stirring occasionally, 30 seconds more. Add the mixed vegetables and 1/4 teaspoon salt and generous pinch pepper, then sprinkle the flour over the top. Cook, stirring frequently, for 2 minutes.
Stir in broth, 1/2 cupful at a time, then add fairlife ultra-filtered milk. Bring to a simmer and cook until root vegetables are tender and liquid is thickened, 8 to 10 minutes. Stir in chicken and pinch each salt and pepper. Remove skillet from heat and set on a rimmed baking sheet.
Place pastry over skillet, allowing corners to hang over sides. Brush with egg wash, then cut six slits in top to vent.
Bake until pastry is deep golden brown and crisp, 25 to 35 minutes. Let pot pie cool on wire rack in pan 10 minutes before serving.
All Coca-Cola Recipes