Preheat oven to 375°.
Heat a Dutch oven coated with cooking spray over medium-high heat. Add onion, and sauté 5 minutes or until tender. Add garlic; sauté 30 seconds. Add squash; sauté 7 minutes or just until tender. Remove from heat; stir in parsley, salt, thyme, and pepper. Add rice, Gruyère, and eggs to squash mixture, stirring until well combined. Spoon the squash mixture into a 13 x 9-inch baking dish coated with cooking spray.
Place bread in a food processor; pulse 10 times or until fine crumbs measure 1/2 cup. Combine breadcrumbs, Parmesan, and butter, tossing to combine. Sprinkle breadcrumb mixture over squash mixture. Bake at 375° for 30 minutes or until topping is lightly browned and filling is set. Let stand 5 minutes before serving.