Preheat the oven to 350 degrees F and grease a 9x13-inch baking dish.
Add 10.5 ounce can condensed cream of chicken soup, 1 cup whole milk, 1/2 cup Duke's mayonnaise, 1/4 cup full-fat sour cream, 1 teaspoon Italian seasoning, 1/2 teaspoon garlic powder, 1/2 teaspoon onion powder, 1/4 teaspoon black pepper, and 1/8 teaspoon coarse salt to the baking dish. Mix until combined.
Add 3 cups fresh broccoli florets, 2 cups shredded rotisserie chicken, 2 cups cooked rice, and 2 cups shredded sharp or extra-sharp Cheddar cheese. Mix until everything is evenly coated.
Scatter 1/2 cup crushed Chicken in a Biskit crackers evenly over the top. Use a pastry brush to dab 2 tablespoons unsalted butter, melted over the crackers.
Bake for 30 minutes, or until heated through and bubbly.