How to Make It
Preheat oven to 400°F. Melt 2 tablespoons of the butter in a large saucepan over medium-high. Add flour; cook, stirring often, 1 minute. Stir in half-and-half; bring to a simmer, and cook, stirring occasionally 2 minutes. Remove from heat. Add Swiss and Gruyère, stirring often, until melted. Stir in cream cheese and sour cream until smooth. Stir in mustard, thyme, and salt. Stir in chicken and ham until combined.
Pour mixture into a 13- x 9-inch baking dish coated with cooking spray. Bake in preheated oven until bubbling and lightly browned, about 30 minutes.
Meanwhile, melt remaining 3 tablespoons butter in a medium skillet over medium-high. Add breadcrumbs, and cook, stirring often, until golden brown, about 3 minutes. Stir in parsley. Sprinkle breadcrumb mixture over casserole; serve hot.