Preheat oven to 400F.
In a skillet over medium-high heat, melt butter. Add diced onion, sliced celery, and diced carrots. Stir well. Cook for about 5-10 minutes, stirring occasionally, until onions are turning translucent and veggies are tender.
Add chicken broth, salt, pepper, and thyme to the skillet. Stir to combine. Bring to a simmer.
In a liquid measuring cup or small bowl, whisk together heavy cream and all-purpose flour until smooth. Pour mixture into the chicken broth, stirring to incorporate. Cook for a few minutes, allowing the liquid to thicken just a bit.
Remove pan from heat. Stir in frozen peas and cooked chicken until combined. Pour mixture into a deep dish pie plate.
Prepare the cornbread topping by combining Jiffy cornbread mix, egg, milk, and vegetable oil in a medium mixing bowl. Mix together until smooth. Add drained corn to the cornbread batter, stirring to combine.
Spoon the cornbread batter over the top of the filling, spreading it evenly.
Bake in preheated oven for about 30-35 minutes, until cornbread topping is golden-brown and cooked through.
Remove from oven and let cool for about 10-15 minutes before serving. This will allow the filling to thicken up a bit more. Enjoy!