Preheat oven to 350 degrees F.
In a greased 2-quart casserole, layer the chicken, eggs, carrots, and peas. Mix the soup, chicken broth, and season with salt and pepper, if desired. Pour over the layers. Stir together the biscuit mix and milk, and pour this over the casserole. Drizzle butter over the topping. Bake until the topping is golden brown, 30 to 40 minutes.