Get Ready: Preheat your oven to 400°F (200°C).
Sauté the Veggies: In a large skillet over medium-high heat, melt the butter or heat the olive oil. Add the diced onion, sliced celery, and diced carrots. Cook for 5-10 minutes, stirring occasionally, until they begin to soften.
Build the Flavor: Pour in the chicken broth, salt, pepper, and thyme. Give it a good stir and bring the mixture to a gentle simmer.
Thicken it Up: In a small bowl, whisk together the heavy cream and flour until smooth. Gradually stir this mixture into the simmering broth in the skillet. Let it cook for a few minutes, stirring, until the filling begins to thicken slightly.
Add Chicken & Peas: Take the skillet off the heat. Stir in the frozen peas and the cooked chicken until everything is well combined. Pour this delicious filling into a deep-dish pie plate.
Whip Up the Cornbread: In a separate medium bowl, combine the Jiffy cornbread mix, egg, milk, and vegetable oil. Mix until smooth. Gently fold in the drained canned corn.
Assemble & Bake: Carefully spoon the cornbread batter evenly over the chicken filling in the pie plate.
Golden Perfection: Bake in your preheated oven for about 30-35 minutes, or until the cornbread topping is beautifully golden-brown and fully cooked through.
Rest & Serve: Remove the pot pie from the oven and let it cool for 10-15 minutes before serving. This short rest allows the filling to set and thicken perfectly. Enjoy your homemade comfort!