Preheat the oven to 350˚F. Lightly grease an 11 X 7~inch baking dish and set aside.
Melt 3 tablespoons of the unsalted butter in a large skillet over medium~high heat. Add the squash, onion, garlic (if using) and salt and cook, stirring often, until center of squash is just tender the onion is translucent, about 10 minutes.
Transfer mixture to a colander set over a bowl and allow to drain for 5 minutes. Discard any liquid.
In a large bowl, combine the eggs, sour cream, and mayonnaise. Stir in the Cheddar and Swiss cheeses, salt, pepper, and thyme and cayenne (if using. Gently fold in the squash mixture until thoroughly combined.
Transfer mixture to the baking dish and smooth on top.
In a medium bowl, microwave the 3 remaining tablespoons of butter on HIGH for 25 seconds until melted. Add the crushed crackers and Parmesan cheese and toss to combine. Add a pinch of cayenne, if desired. Sprinkle the cracker mixture over the squash mixture, covering it completely. Bake in preheated oven for 20 minutes until golden brown.