Preheat oven to 425 F. Spray a large casserole dish with nonstick cooking spray and set aside. Heat 1 Tbsp. of the olive oil in a large skillet over medium-high heat. Once hot, add onions and garlic and cook for 4-5 minutes or until the onion has soften and beginning to become translucent.
Add chopped squash and season with salt and pepper. Cook squash mixture, stirring as needed to cook evenly, for approximately 10 minutes or until squash is slightly tender and fragrant. Transfer squash mixture to prepared casserole dish.
While squash is cooking, add egg whites, Greek yogurt, rosemary, nutmeg and sage to a medium mixing bowl, whisk to combine. In another mixing bowl, combine breadcrumbs, Parmesan cheese and fresh ground pepper. Stir to combine. Pour egg mixture evenly over top of squash in casserole dish. Finish casserole dish by sprinkling breadcrumb mixture evenly over top.
Bake squash casserole in preheated oven for 25-30 minutes or until squash is tender, the casserole is bubbling and breadcrumb topping is golden brown.