Lightly spray a 9x13" casserole dish with non stick cooking spray. Spread the chicken evenly out over the bottom of the dish. Next, do the same with the ham. Lay the sliced cheese evenly out over the meats.
Heat a large skillet over medium heat, add the butter. Once melted, whisk in the flour- stirring & cooking for 60 seconds to cook out the floury taste.
Pour the milk in 1/2 cup at a time, whisking until the mixture comes together & thickens before adding the next bit. Repeat until the roux is finished and smooth. Raise the heat and bring the mixture to a boil, whisking often until thickened.
Remove the skillet from heat, and whisk in the rest of the sauce ingredients until smooth. Pour the sauce out evenly over the casserole dish. You can use a spatula to smooth it out a bit and so that it seeps down the outer edges and into any cracks.
Add the bread crumbs & melted butter to a small mixing bowl. Whisk them together until evenly incorporated. Spread the breading mix evenly out over the top of the casserole dish.
Bake the casserole at 350 degrees for 45 minutes. Let the dish rest for 8-10 minutes, allowing the sauce to thicken, before scooping and serving.