Set the oven's temperature to 450°F. Place a 10-inch pie dish or an 11-by-7-inch baking dish on a baking sheet.
Take a large skillet. Place it over medium heat. Add butter to that skillet and let it melt. Once the butter is melted, add the onion, celery, and carrots that and simmer for 5 minutes, stirring regularly, until softened.
Add the frozen peas and cook for 1 more minute, then sprinkle the top with the salt, pepper, flour, and Herbes de Provence. Cook and stir the vegetables until thoroughly coated.
Add the chicken broth, milk, and bouillon all at once. Stir everything together and simmer for 2 minutes, or until heated through and bubbling.
Remove from heat and add the chicken and parsley. Transfer the mixture to the pie dish right away.
Now carefully unroll the pie dough and lay it on top of the chicken mixture. Flute and seal the edges of the plate. To release steam, make many slits in the dough using a sharp knife. To give the crust a glossy sheen before baking, you can whisk the egg yolk and water together and brush it over the top.
Bake the pot pie for 12 to 15 minutes, or until the crust turns brown and the filling bubbles.
Your delectable Cracker Barrel's Chicken Pot Pie is ready. Bon Appetit!