Preheat oven to 350°F. Coat an 8-inch-square baking dish with cooking spray.
Heat 1½ tablespoons oil in a large nonstick skillet over medium-high heat. Add sliced zucchini, sliced shallots and ¼ teaspoon plus ⅛ teaspoon salt; cook, stirring often, until the zucchini is just tender and the liquid has evaporated, 10 to 12 minutes.
Stir in 1 package cream cheese; cook, stirring constantly, until melted and creamy, 1 to 2 minutes.
Transfer the zucchini mixture to a large bowl. Add 1½ cups corn, ½ cup cottage cheese, 1 teaspoon garlic powder, ½ teaspoon pepper and 1 egg; stir until well combined. Transfer to the prepared baking dish.
Combine ½ cup panko, ¼ cup Parmesan and the remaining 1½ teaspoons oil in a small bowl; stir until the panko is evenly coated. Sprinkle over the casserole.
Bake until the topping is golden brown and the casserole is set, 35 to 40 minutes. Let stand for 10 minutes before serving.
