Heat oven to 400°F (200°C). Lightly grease a 9x13-inch baking dish.
Bring a large pot of salted water to a boil and cook 1 pound penne pasta according to the package directions until al dente. Drain and transfer pasta to the prepared baking dish.
Meanwhile, melt 1/4 cup salted butter in a medium-sized saucepan over medium heat. Whisk in 1/4 cup all-purpose flour and 1 tablespoon minced garlic, then cook for 1 minute, whisking constantly.
While whisking, gradually pour in 2 cups chicken broth and 2 cups heavy cream. Then whisk in 2 tablespoons dijon mustard, 1 tablespoon brown sugarand 1 tablespoon apple cider vinegar. Season with 1/4 teaspoon salt and 1/4 teaspoon black pepper. Bring to a simmer over medium heat and simmer, stirring occasionally, for 3 to 5 minutes, until the mixture has thickened.
Gradually stir in 1 cup shredded Swiss cheese until it is fully melted into the sauce. Remove saucepan from heat.
Sprinkle 16 ounces shredded cooked chicken and 16 ounces cubed ham evenly over the pasta in the baking dish. Pour the sauce over these ingredients, ensuring everything is well coated.
In a small bowl, stir together 1/2 cup panko bread crumbs, 2 tablespoons salted butter, and 1/2 teaspoon garlic powder. Sprinkle this mixture over the top of the casserole to cover.
Bake, uncovered, in the preheated oven for 15 to 20 minutes, until the topping is lightly browned. Serve hot.
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Notes
Ham is sold in packages in the refrigerated meat section of the grocery store, or you can cube leftover ham.
For the shredded cooked chicken, use leftovers, purchase pre-cooked chicken, or use shredded rotisserie chicken.