Preheat the oven to 375 degrees F. Spray the inside of a 9-inch x 13-inch casserole dish with cooking spray and set aside.
Place chicken in a mixing bowl and season with salt and pepper. Toss to coat, being sure every piece is well seasoned.
Heat olive oil in a large skillet over medium heat. Add chicken to the pan and cook for 5-8 minutes or until no longer pink. Transfer the cooked chicken to a bowl with all the juices and seasonings; set aside.
Add butter to the same skillet and melt over medium heat. Add the onion, celery, carrots, and garlic. Cook until transparent and tender about 3- 5 minutes. Add the salt, pepper, poultry seasoning, and thyme, and mix. Cook for 2 more minutes.
Add flour to the onion mixture and mix to coat. Whisk in milk and chicken stock until well blended. Continue whisking until it comes to a boil. Reduce heat to medium-low and allow the mixture to thicken and reduce, about 2 minutes.
Add chicken and its juices to the skillet, along with the peas, and mix well. Remove from heat.
Transfer mixture to the prepared baking dish. Top mixture with biscuits, placing them evenly on top. In a small bowl, beat together egg and water. Brush egg mixture on top of the biscuits.
Bake casserole for 20 minutes or until mixture is bubbling and the top of the biscuits are golden brown.
Remove from the oven and let cool for 5 minutes. Brush melted butter on top of the biscuits and allow it to cool for another 5 minutes before serving. Garnish with fresh thyme leaves, if desired.