Combine chicken, carrots, celery, and peas in a skillet over medium-high heat. Saute until vegetables are tender and chicken is no longer pink in the center, 7 to 10 minutes. Transfer mixture to a casserole dish.
Preheat the oven to 350 degrees F (175 degrees C).
Melt butter in the same skillet; reduce heat to medium. Stir in flour, dried onion, salt, pepper, and celery seed. Add chicken broth and milk slowly; cook and stir until thickened, about 20 minutes. Pour mixture into the dish, almost covering the chicken and vegetables. Cover vegetables with biscuit pieces.
Bake in the preheated oven until biscuits have raised and browned, about 30 minutes.