Preheat the oven to 350 degrees F (175 degrees C). Grease a large baking dish.
Combine chicken, carrot, celery, and bouillon in a large pot and add enough water to cover. Bring to a boil, cover, and cook until chicken is no longer pink in the centers, 10 to 15 minutes. Drain, reserving chicken and broth in another pot or bowl.
Melt butter in the same pot over medium heat. Cook onion and garlic in the hot butter for 5 minutes. Stir in flour, poultry seasoning, basil, thyme, and pepper. Stir in chicken broth and milk slowly. Add chicken mixture and peas. Simmer over medium-low heat until thick, 10 to 15 minutes. Pour mixture into the prepared baking dish.
Bake in the preheated oven until mixture is bubbling, 20 to 25 minutes. Remove from the oven and place biscuits on top. Cover and bake for 15 minutes. Uncover and continue baking until biscuits are golden brown, 15 to 20 minutes more.