Preheat the oven to 375°F.

Melt 2 tablespoons of butter in a 10-inch cast iron skillet over medium-high heat. Add the potato, onion, and carrots 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 in the microwave 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 for 15 minutes. Meanwhile, melt the remaining 6 tablespoons of butter in a large saucepan over medium heat. Whisk in the flour and cook, whisking constantly, for 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.