Preheat the oven to 375°F. Lightly grease a 9x9-inch pan. Combine cheddar, Parmesan, garlic, oregano, and 2 tablespoons basil in a large bowl. Season mixture with salt and pepper and set aside.
To assemble casserole: Arrange ½ of the zucchini slices in the pan. Sprinkle ¼ of the cheese mixture on top. Next, arrange ½ of the tomato slices. Sprinkle with another ¼ of the cheese mixture. Then layer the remaining zucchini slices on top. Sprinkle another ¼ of the cheese mixture. Finally, add the remaining tomato slices and top with the last of the cheese mixture.
To make topping: Melt butter in a skillet over medium heat. Add onions and cook until translucent. Add gluten-free breadcrumbs and cook until they have absorbed the butter and just start to become very lightly toasted. Sprinkle bread crumb mixture on top of casserole.
Cover loosely with foil that has been lightly oiled and bake in preheated oven for 25 minutes. Remove foil and bake until the top is nicely browned and vegetables are tender, about 15-20 minutes longer. Let sit for at least 15 minutes before serving. Garnish with remaining fresh basil and fresh chives.