Step 1: Preheat the Oven and Melt the Butter - Preheat your oven to 350°F. Put the ½ cup of unsalted butter into a 9 by 13 inch baking dish, then place the dish in the oven just long enough for the butter to melt. Keep an eye on it because you are not trying to brown the butter. You simply want it fully melted and ready to coat the bottom of the dish. Carefully remove the hot pan from the oven and gently tilt or swirl it so the butter covers the bottom as evenly as possible.
Step 2: Layer in the Chicken - Scatter the 3 cups of shredded rotisserie chicken evenly over the melted butter. Try to spread it all the way to the corners so every serving gets a good amount of chicken. You do not need to press it down or mix it with the butter. In fact, one of the biggest things to remember with Chicken Cobbler is that the layers are supposed to stay separate while you assemble it. The oven will bring everything together as it bakes.
Step 3: Add the Peas and Carrots - Sprinkle the frozen peas and carrots evenly over the chicken. They can go straight into the casserole from the freezer, so there is no need to thaw, drain, or cook them first. I like to make sure the vegetables are spread around rather than sitting in one big pile because that gives you a little color and sweetness in every scoop. Once they are in the dish, leave the layers alone and move on to the creamy portion.
Step 4: Add the Cream of Chicken Soup and Stock - Dollop the cream of chicken soup evenly across the vegetables. It does not have to look perfectly smooth because it will loosen as the casserole heats. Slowly pour the chicken stock over the top, moving around the dish as you pour so the liquid is distributed as evenly as possible. Do not stir. I know it can feel strange to leave everything sitting in layers, especially when your instinct says casserole ingredients should be mixed together, but that separation is what helps create the creamy filling underneath the biscuit topping.
Step 5: Mix the Biscuit Topping - In a large mixing bowl, whisk together the Bisquick baking mix and whole milk until the mixture is smooth. Make sure you scrape around the bottom and sides of the bowl so you do not leave dry pockets of baking mix behind. The batter will be pourable, which is exactly what you want. You are not making traditional rolled biscuits here. This batter spreads over the casserole and bakes into one big tender topping that you can scoop right along with the chicken filling.
Step 6: Pour on the Biscuit Batter - Carefully pour the Bisquick mixture evenly over the casserole. Move slowly from one side of the dish to the other so you cover as much of the surface as you can. Again, do not stir. The casserole may look a little unusual at this stage because you can still see distinct layers, but that is completely normal. As it bakes, the liquid underneath thickens and bubbles while the biscuit mixture rises and sets across the top.
Step 7: Bake Until Golden and Bubbling - Place the casserole in the oven uncovered and bake for 55 to 60 minutes. You are looking for a golden biscuit topping that appears cooked through rather than wet in the center. Around the edges, the creamy chicken filling should be hot and bubbling. If the topping starts getting darker than you would like before the middle is done, loosely cover the dish with foil for the final portion of the baking time. That lets the center keep cooking without pushing the top too far.
Step 8: Rest Before Serving - Take the Chicken Cobbler out of the oven and let it rest for about 10 minutes before serving. This is one of those little steps that is easy to skip when everyone is standing around asking when dinner is ready, but it makes a difference. The filling is extremely hot right out of the oven, and the resting time gives the creamy gravy a chance to thicken slightly. Once it has settled, scoop generous portions into bowls or onto plates and make sure everyone gets some of that golden topping.