Preheat your oven to 350°F.
Melt 2 tablespoons of butter in a large skillet over medium-high heat.
Add the zucchini and onion and cook for about 7 minutes, stirring occasionally, until the zucchini is tender and the onions are translucent. Transfer the mixture to a large bowl.
In the same skillet used to cook the zucchini and onion, melt the remaining 2 tablespoons of butter over medium heat.
Whisk the flour into the melted butter and cook for about 1 minute. (It will look like lumpy paste. That's okay! Trust the process.)
Whisk in the broth and half and half until no lumps remain. After a minute or two, it will turn to a thick gravy consistency.
Sprinkle in the garlic powder, salt, and pepper, and stir to combine.
Pour the sauce into the bowl of zucchini and onion.
Add 1 cup of the shredded cheese, the egg, and cracker crumbs. Stir gently until well combined.
Pour the mixture into a greased 8X8 inch casserole dish.
Sprinkle the remaining 1/2 cup of shredded cheese evenly over the top.
Bake for 35-40 minutes, until golden and bubbly.
Let it cool for a few minutes before serving.