Preheat oven to 350°. Coat a 13"-by-9" baking dish and a rimmed baking sheet with cooking spray.

Arrange prosciutto on prepared baking sheet in an even layer with no overlap. Bake until crispy, 10 to 15 minutes. Let cool (they will continue to crisp while cooling).

Meanwhile, in a large saucepan over medium heat, melt butter. Whisk in flour and let bubble until light golden brown and toasted, about 2 minutes. Pour in broth and milk and simmer, whisking occasionally, until thickened, 4 to 6 minutes. Whisk in mustard, salt, and pepper.

Stir chicken and ham into sauce. Simmer, stirring occasionally, until chicken is cooked through, 9 to 11 minutes. Stir in 2 cups cheese and immediately transfer mixture to prepared baking dish. Top with remaining 2 cups cheese.

Place cooled prosciutto in a small bowl. Using the handle of a wooden spoon, crush into fine crumbs. Add panko and toss to combine. Sprinkle prosciutto mixture evenly over baking dish.

Bake until filling is bubbling and crumbs are golden brown, 30 to 35 minutes. Top with parsley and serve.