Preheat oven to 375 degrees.
In a large ovenproof skillet melt the butter. Saute the onion, carrot, celery, salt, pepper and thyme until vegetables are crisp tender.
Stir in 6 tbsp flour and cook about 2 minutes or until thick paste forms and mixture is beginning to brown.
Gradually stir in the chicken broth and half & half or milk. Cook and stir 1-3 minutes or until bubbly and thickened.
Stir in the chicken and frozen peas and remove from the heat.
Separate the biscuits and cut into fourths. Top the chicken mixture with the biscuits.
Bake uncovered for 20-25 minutes or until biscuits are golden brown. Let stand for 5-10 minutes and serve.
NOTES: *Don't overcook the vegetables. They will continue cooking as the dish bakes in the oven, so saute them just until they begin to soften. *If the filling seems too thick, add a splash of chicken broth. It it's too thin, let it simmer a few extra minutes before adding the biscuits. *Leave a little space between the biscuits. This helps them bake evenly and become golden brown on top. *Check the biscuit doneness. The tops may brown before the centers are fully cooked, so test one biscuit before removing the dish from the oven. *Customize the vegetables. Peas, carrots, corn, green beans, and mushrooms all work well in this recipe. *Allow the skillet to sit for 5-10 minutes after baking so the filling can thicken slightly.
Storage Tips: Refrigerate: Store any leftovers in an airtight container in the refrigerator for up to 3-4 days. Freeze: The chicken filling freezes well for up to 3 months. For best results, freeze the filling separate and add fresh biscuits when ready to bake. Reheat: Warm leftovers in the oven at 350 degrees until heated through, or microwave individual portions for a quick meal.