Heat the oven to 350 °F and grease a 9x13-inch casserole dish. Coat the base and corners lightly so the creamy edges release easily after baking.

Whisk the mayonnaise, heavy cream, and cream cheese in a small bowl until completely smooth. Press any cream cheese against the side of the bowl until no firm white lumps remain.

Stir the grated parmesan cheese, garlic powder, and ground black pepper into the cream cheese mixture. The sauce should look thick, creamy, and evenly seasoned.

Combine the shredded Swiss cheese, sliced Black Forest ham, and shredded rotisserie chicken in a large bowl. Separate the ham as you toss so it disperses through the chicken instead of clumping together.

Pour in the chicken broth and toss the mixture gently. The chicken should take on a light coating of moisture without sitting in a pool of liquid.

Add the creamy sauce and fold until the chicken and ham are thoroughly coated. Look for an even, glossy coating across the bowl before transferring the mixture.

Spread the mixture in the prepared dish and bake for 25 minutes. Remove it when the edges bubble actively and the top has light golden-brown speckles.