Preheat the oven to 350°F.
Lightly grease a 9x13-inch baking dish and arrange the chicken and zucchini evenly across the bottom.
In a mixing bowl, combine the butter, eggs, heavy cream, and seasonings.
Using an electric mixer, blend until smooth.
Gently fold in both cheeses, then pour the mixture evenly over the chicken and zucchini.
In a separate bowl, combine the Cheez-It crackers with the melted butter, tossing to coat.
Sprinkle the cracker mixture evenly over the top of the casserole.
Bake for 35-40 minutes, or until the casserole is set and the topping is golden brown.