Preheat oven to 450°F with racks in top third and lower third positions. Using a sharp knife, score cut sides of zucchini halves in a crosshatch pattern, cutting about ⅛-inch deep. Pat the zucchini dry; place scored-sides up on a large rimmed baking sheet.
Stir 1 tablespoon oil, ¼ teaspoon garlic and ¼ teaspoon pepper together in a small bowl. Brush the mixture on both sides of the zucchini. Arrange the zucchini around the pan edges, scored-sides down. Roast on the lower rack until almost tender, about 10 minutes. Move the pan to the top rack; increase oven temperature to broil. Broil until tender and browned in spots, 8 to 10 minutes.
Meanwhile, stir softened butter, 1 tablespoon herbs, ½ teaspoon lemon zest, ¼ teaspoon salt and the remaining ½ teaspoon garlic together in a small bowl.
Remove the zucchini from the oven; flip and immediately brush with the butter mixture. Sprinkle with 1 tablespoon Parmesan and the remaining ¼ teaspoon salt.
