Add the cheese layer: Lay the Swiss cheese slices over the ham, overlapping slightly so they cover most of the surface. Sprinkle 1/4 cup of the grated Parmesan over the Swiss.
Make the low carb cream sauce: In a medium saucepan over medium-low heat, combine the heavy cream, cream cheese cubes, Dijon mustard, smoked paprika, nutmeg (if using), and the remaining 1/2 teaspoon kosher salt. Whisk gently as the cream cheese melts, 4–6 minutes, until the sauce is smooth and just starting to bubble around the edges. Remove from heat.
Pour the warm cream sauce evenly over the layered chicken, ham, and cheese in the baking dish, using a spatula to nudge it into the corners so everything is lightly coated.
Prepare the cheesy topping: In a small bowl, stir together the melted butter, remaining 1/4 cup grated Parmesan, and the 1/2 cup finely grated Parmesan or Parmesan–mozzarella blend. This creates a rich, low carb alternative to a breadcrumb topping. Sprinkle the mixture evenly over the top of the casserole.
Bake the casserole: Place the dish in the preheated oven and bake for 25–30 minutes, or until the chicken is cooked through (internal temperature reaches 165°F/74°C), the sauce is bubbling, and the top is golden in spots.
