Preheat the oven to 400 degrees F (204 degrees C). Lightly grease a 2-quart rectangular baking dish with nonstick cooking spray.
Heat oil in an extra-large skillet over medium. Add onion; cook and stir until softened, 4 to 5 minutes. Add garlic and cook until fragrant, 1 minute.
Add zucchini, bell peppers, and salt. Cook, stirring occasionally, until tender, about 8 minutes. Stir in diced tomatoes.
Whisk together chicken stock, cornstarch, Herbes de Provence, and pepper in a small bowl until well combined. Pour into skillet and bring to a boil over medium-high heat.
Stir in chicken. Transfer mixture to prepared baking dish.
Quickly roll puff pastry to fit the top of the baking dish and lay on top of chicken and vegetable mixture. Brush with beaten egg. Slice or pierce a few holes along the top.
Bake in the preheated oven until pastry is puffed and golden brown, about 20 minutes.
Let pie stand for at least 10 minutes before serving. Garnish with fresh parsley. Recipe developed by Barrett Heald