Add the chicken, frozen peas and carrots, frozen broccoli, both cans of soup, and the milk to an oven-proof skillet. Mix until combined and spread evenly in the pan.
Keeping the vegetables frozen helps prevent the filling from getting watery.
In a separate bowl, combine the Cheddar Bay Biscuit Mix and shredded cheddar cheese. Remove the seasoning packet from the box and set it aside for later.
Add the cold water and stir just until the dough comes together. Do not overmix or the biscuit topping can turn dense instead of fluffy.
Drop dollops of the biscuit mixture on top of the chicken filling, covering as much of the surface as you can. Rotisserie chicken works especially well here if you want a quick shortcut.
Bake for 35 minutes, until the biscuits are cooked through and golden on top.
Remove from the oven. Stir together the melted butter and the reserved seasoning packet, then use a pastry brush to coat the tops of the biscuits with the herb butter. Do not skip the seasoning packet, since it gives the topping that classic cheddar bay flavor.
Let the skillet stand for 10 minutes before serving so the filling can thicken slightly. Top with chopped fresh parsley if desired.