Prepare the pasta and baking dish. Preheat the oven to 400°F (200°C). Lightly grease a 9 × 13-inch baking dish. Cook the penne according to the directions on the package, then drain thoroughly. Transfer the cooked pasta to the prepared dish and arrange it in an even layer.

Begin the cheese sauce. Place ¼ cup unsalted butter in a medium saucepan over medium heat and allow it to melt. Add the minced garlic and all-purpose flour. Cook, stirring, for 1–2 minutes, until the garlic becomes aromatic.

Add the liquids and seasonings. Slowly whisk the chicken broth and heavy cream into the flour mixture, continuing until the sauce is smooth. Stir in the Dijon mustard, brown sugar, apple cider vinegar, salt, and black pepper.

Thicken and finish the sauce. Bring the mixture to a gentle simmer. Cook for 2–3 minutes, stirring occasionally, until the sauce thickens slightly. Take the saucepan off the heat and add the shredded Swiss cheese, stirring until completely melted and incorporated.

Assemble the casserole. Distribute the cooked chicken evenly over the penne. Scatter the chopped ham over the chicken, then pour the prepared Swiss cheese sauce across the casserole, making sure the pasta, chicken, and ham are evenly covered.

Make the breadcrumb topping. Combine the panko breadcrumbs, melted butter, and garlic powder in a small bowl. Stir until the crumbs are evenly coated, then sprinkle the mixture uniformly over the casserole.

Bake. Place the casserole in the preheated oven and bake uncovered for 15–20 minutes. It is ready when the sauce is bubbling and the breadcrumb topping has developed a light golden-brown color.

Serve. Remove the baking dish from the oven and allow the casserole to cool briefly before serving. Serve while hot.