Preheat your oven to 375°F. Line a rimmed baking sheet with parchment paper or lightly grease a 9-by-5-inch loaf pan.
In a large bowl, combine the breadcrumbs and milk. Let them sit for 2–3 minutes to soften. Add the ground chicken, egg, Parmesan, minced garlic, onion powder, garlic powder, parsley, paprika, salt, black pepper, and Dijon mustard. Mix gently until just combined.
Place the mixture on a sheet of parchment paper and flatten it into a rectangle. Arrange the ham slices over the meat mixture, then place the Swiss cheese on top. Roll the meat mixture into a log and pinch the seam closed.
Transfer the loaf seam-side down to the prepared baking sheet. Bake for 55–65 minutes until the internal temperature reaches 165°F.
While the meatloaf bakes, melt the butter in a saucepan over medium-low heat. Add minced garlic and cook for 30 seconds. Whisk in flour and cook for 1 minute. Gradually whisk in milk and heavy cream, cooking until thickened. Stir in Dijon mustard, Swiss cheese, Parmesan, and black pepper.
Remove the meatloaf from the oven and let it rest for 10 minutes before slicing.
Transfer the meatloaf to a serving platter and pour the creamy sauce over the top or serve it on the side.
Slice and serve immediately while warm.
Notes
For easier slicing, let the meatloaf rest before cutting.
If the top browns too quickly, cover it loosely with foil.
Adjust the thickness of the sauce with milk as needed.