Preheat the oven to 375°F.
Melt 2 tablespoons of the butter in a 10-inch cast-iron skillet over medium-high. Add the potato, onion and carrot, and cook, stirring occasionally for 6 minutes. Add the bell pepper, mushrooms, garlic, crushed red pepper, 1/2 teaspoon of the salt and 1/4 teaspoon black pepper. Reduce the heat to medium and cook, stirring often, until the potatoes are almost tender, about 8 minutes.
Cook the haricots verts according to the package directions. Cool slightly, and cut into 1-inch pieces. Add the haricots verts, chicken and peas to the potato mixture. Remove skillet from the heat and set aside.
Remove the pie crust from the refrigerator and let stand 15 minutes. Meanwhile, melt the remaining 6 tablespoons butter in a large saucepan over medium heat. Whisk in the flour and cook, whisking constantly, 1 minute. Gradually whisk in the chicken stock and cook, whisking constantly, until the mixture thickens, about 10 minutes. Whisk in the heavy cream, hot sauce and the remaining 3/4 teaspoon salt and 1/2 teaspoon black pepper. Pour the cream sauce over the chicken mixture in the skillet, and stir gently to combine.
Unroll the pie crust and fit it over the filling, fluting around the edges, if desired. Brush the crust lightly with the beaten egg and cut 4 small slits for the steam to escape. Bake until the filling is bubbly and the crust is golden brown, about 30 minutes. Let stand about 10 minutes before serving. Garnish with the chopped parsley and serve with the hot sauce, if desired.
Excerpt from Valerie’s Home Cooking by Valerie Bertinelli. Copyright © 2017 by Valerie Bertinelli. Used with permission by Oxmoor House. All rights reserved.