Preheat oven to 425 degrees F. Lightly grease a 13×9 inch casserole dish.
Heat a skillet over medium-high heat. Add the olive oil to the pan, followed by the finely diced onion, carrot, and celery to the skillet, and cook for 5-7 minutes.
Add the finely minced garlic and continue to cook for 30 seconds.
Add 4 tablespoons of butter to the center of the skillet and cook until it has melted.
To the butter, add salt, pepper, and flour. Cook for 1 minute.
Pour in the chicken broth, stir all ingredients together. Bring to a boil and cook until the sauce has thickened, approximately 3-5 minutes.
Stir in the heavy cream, cheddar cheese, and cooked chicken.
Spoon the chicken mixture into the 9×13 inch casserole dish.
Mix the cheddar bay biscuit mix up according to package instructions.
Evenly top the chicken mixture with heaping spoonfuls of the biscuit dough.
Make the herb butter mixture according to package instructions.
Bake for 30-35 minutes or until the biscuits are golden brown.
Remove from the oven and brush the butter over the cooked biscuits. Serve hot.