Step 1

Preheat oven to 350°F. Melt 3 tablespoons of the butter in a large skillet over medium-high. Add squash, onion, and 1 teaspoon of the salt; cook, stirring often, until center of squash is just tender and liquid has evaporated, about 10 minutes. Transfer mixture to a colander set over a bowl. Drain 5 minutes; discard any liquid.

Step 2

Stir together eggs, sour cream, Cheddar and Swiss cheeses, mayonnaise, thyme, pepper, and remaining 1 teaspoon salt in a large bowl. Gently fold in squash mixture. Spoon into a lightly greased 11- x 7-inch (2-quart) baking dish.

Step 3

Microwave remaining 3 tablespoons butter in a medium-size microwavable bowl on HIGH until melted, about 25 seconds. Toss together crackers, Parmesan cheese, and melted butter until combined; sprinkle over casserole. Bake in preheated oven until golden brown, about 20 minutes.