Preheat oven to 375°F (190°C).
In a large bowl, combine chicken, carrots, celery, peas, and onion.
In a saucepan, whisk together flour and chicken broth until smooth. Bring to a simmer over medium heat, stirring constantly. Stir in milk, salt, and pepper. Cook until thickened, about 2-3 minutes.
Pour the sauce over the chicken and vegetables and mix well. Transfer to a 9x13 inch baking dish.
In a small bowl, combine biscuit mix and milk. Stir in melted butter.
Drop spoonfuls of biscuit topping over the chicken mixture.
Bake for 30-40 minutes, or until the topping is golden brown and the casserole is bubbly.