Cook first 3 ingredients in boiling water to cover in a Dutch oven 25 minutes or until squash is very tender. Drain well, and mash mixture with a fork.
Crush 10 crackers, and stir into squash mixture; stir in 1/2 cup cheese and next 5 ingredients. Spoon mixture into a lightly greased 11- x-7-inch baking dish.
Crush remaining 6 crackers, and sprinkle over casserole; sprinkle remaining 1 cup cheese evenly over casserole.
Bake, uncovered, at 350° for 30 minutes or until cheese melts and casserole is bubbly.
Note: To make ahead, prepare recipe as directed; do not top with crackers or cheese. Cover and chill overnight. Remove from refrigerator; let stand 30 minutes. Uncover and top with crackers and cheese; bake as directed.