Place zucchini in a pot with about 1 inch of water. Bring to a boil, and cook until tender but still firm, about 10 minutes. Drain zucchini and transfer to a large bowl. Mash with a fork, then transfer to a fine mesh strainer or sieve, pressing to release excess water. Return to mixing bowl.
Melt 4 tablespoons butter in a large skillet over medium-high heat. Add onion and garlic, and cook until lightly browned being careful not to burn the garlic. Remove from heat, stir into the zucchini. Mix in the eggs, Parmesan cheese, bread crumbs, and basil. Season with salt and pepper.
Butter an 8 inch square baking dish with remaining butter. Pour the zucchini mixture into the dish, and spread evenly. Bake in the preheated oven until firm in the center and lightly browned on top, about 45 minutes. Allow to cool, cut into squares, and serve.
3 pounds zucchini, cubed
5 tablespoons unsalted butter, divided
1 large onion, chopped
4 garlic cloves, minced
2 eggs, beaten
1/2 cup freshly grated Parmesan cheese
1/2 cup fresh white bread crumbs
1/4 cup chopped fresh basil leaves, packed salt and pepper to taste