Preheat oven to 350°F (175°C). Grease a 9x13-inch baking dish.
In a large skillet, melt 2 tablespoons butter over medium heat. Add onion and cook until softened, about 3 minutes. Add squash and cook, stirring occasionally, until tender, about 5-7 minutes. Remove from heat.
In a large bowl, combine cream of chicken soup, sour cream, cheddar cheese, Parmesan cheese, salt, and pepper. Stir in the cooked squash mixture until well combined.
Spread the mixture evenly into the prepared baking dish.
In a small bowl, mix crushed crackers with melted butter. Sprinkle evenly over the casserole.
Bake for 25-30 minutes, until bubbly and topping is golden brown. Let stand 5 minutes before serving.
Tips
For a lighter version, use reduced-fat soup and sour cream.
Can be assembled a day ahead; refrigerate and add topping just before baking.
Leftovers keep refrigerated for up to 3 days; reheat in oven or microwave.