Slice each zucchini in half lengthwise to create 4 “”steaks.”” Score the flesh side of each steak diagonally, about 1/4″” deep and at 1/2″” intervals. Rotate the steaks 90° and score again to form a crosshatch pattern. Sprinkle the scored sides with 1 teaspoon of salt and let them sit for about 15 minutes to release moisture.
Preheat the oven to 425°F and place a rack in the center. In a large skillet over medium heat, cook the garlic, red pepper flakes, and 2 tablespoons of olive oil, stirring until the garlic becomes fragrant, about 1 to 2 minutes. Transfer the garlic oil to a small bowl.
In the same skillet over medium-high heat, add 1 tablespoon of olive oil. Pat the zucchini dry and place 2 halves flesh side down in the skillet, cooking until golden brown on the bottom, about 2 to 3 minutes. Move them to a baking sheet with the flesh side up and repeat with the remaining zucchini and olive oil.
Brush the steaks with the garlic oil and bake until the zucchini is tender in the center, about 8 to 10 minutes. Top with mozzarella and Parmesan.
Set the broiler to high and broil the zucchini, watching closely, until the cheese is melted and browned, about 2 to 3 minutes.
Transfer the zucchini to a platter and garnish with basil and additional red pepper flakes.