In a large pot, bring the squash to boil. Reduce to a simmer until squash is soft.
In a large bowl, mash the softened squash. Mix in the mayonnaise, onion, egg, brown sugar, salt and pepper. Pour the mixture into a 2 quart baking dish.
In a medium bowl, mix together crackers, Parmesan and butter. Sprinkle over the squash mixture.
Bake uncovered in the preheated oven for 35 to 45 minutes, until the topping is lightly brown.