Preheat the oven to 400°F.

Heat a 12-inch ovenproof cast-iron skillet over medium-high heat and add olive oil to the bottom of the skillet.

Add the onion and celery to the skillet. Sauté for five to seven minutes, until the onion is translucent and the celery is tender.

Reduce the heat to medium-low. Add the fresh minced garlic. Sauté for up to two minutes.

Transfer the cooked onion, celery, and garlic to a bowl or plate and set aside.

Return the skillet to the stovetop and keep the heat at medium-low, add the 2 tablespoons of butter.

Once the butter has melted, whisk in the 3 tablespoons of flour. Continue whisking until the flour has absorbed the butter, for about 30 seconds to 1 minute.

Keeping the heat at medium-low, slowly whisk in the chicken stock. Once the mixture is smooth, slowly whisk in the heavy cream and continue whisking.

Allow the broth mixture to come to a low simmer and begin to thicken. This may take 3 to 5 minutes.

Once the broth mixture is thickened, whisk in the kosher salt, black pepper, rosemary, and thyme leaves.

Once the seasoning is well incorporated, remove the skillet from the heat.

Return the onion, garlic, and celery back to the broth mixture. Use a large wooden spoon to stir the mixture.

Continue to stir, then add the frozen peas, carrots, and chicken. Stir until the peas and carrots and the chicken are entirely coated and evenly distributed. Leave the chicken mixture in the skillet.

Unroll the premade pie crust and gently place it on top of the chicken mixture. If needed, gently stretch the pie crust so it covers the chicken mixture and touches the sides of the skillet. Using a fork, press the edges of the pie crust to the edges of the skillet. Make a few slits in the top of the crust; this is to allow the heat to escape.

Whisk together the egg and water to make an Egg Wash. Using a pastry brush, brush the egg wash on top of the pie crust.

Bake the pot pie for 30 minutes or until the pie crust is golden brown.

Melt the final tablespoon of butter. After removing the pan from the oven, using a pastry brush, evenly coat the top of the pie crust topping.