Gradually pour in the chicken broth and milk, scraping the pan to lift any browned bits. Bring the mixture to a simmer and allow it to thicken for approximately 4-5 minutes.
Stir in the shredded chicken, frozen peas, and corn kernels. Adjust salt and pepper if needed. Spread the filling evenly in a 9×13-inch baking dish. Arrange the separated biscuits on top in a single layer.
Melt the remaining 2 tablespoons of butter and brush it over the biscuits. Let the casserole cool for a 10-15 minutes before serving.