Preheat oven to 425 degrees F. Lightly grease a 13x9 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 and stir all ingredients together. Bring to a boil and cook until the sauce has thickened, approximately 3-5 minutes.
Stir in the cooked chicken.
Spoon the chicken mixture into the 9x13 inch casserole dish.
Remove the biscuits from the package and peel each biscuit apart at the center to create two thinner ones.
Evenly top the chicken mixture with the biscuits.
Place the remaining butter in a small microwave-safe dish and microwave for 30 seconds or until melted. Add the thyme and stir together.
Brush the thyme butter over the biscuits
Bake for 12-15 minutes or until the biscuits are golden brown.
Remove from oven and let cool for 5 minutes before serving.