Using a sharp knife, slice each zucchini in half lengthwise, yielding 4 'steaks.' Score flesh side of each steak ¼' deep diagonally at ½' intervals. Rotate steaks 90° and score diagonally again to create a crosshatch pattern.

Season steaks on scored sides with 1 tsp. salt. Let sit to allow zucchini to release moisture, about 15 minutes.

Arrange a rack in center of oven; preheat to 425°. In a large skillet over medium heat, cook garlic, red pepper flakes, and 2 Tbsp. olive oil, stirring, until garlic is fragrant, 1 to 2 minutes. Scrape garlic oil into a small bowl.

In same skillet over medium-high heat, heat 1 Tbsp. olive oil. Pat zucchini dry. Arrange 2 halves flesh side down in skillet and cook, undisturbed, until golden brown on the bottom, 2 to 3 minutes. Transfer to a baking sheet flesh side up. Repeat with remaining zucchini and 1 Tbsp. olive oil.

Brush steaks with garlic oil. Bake until tender in the center, 8 to 10 minutes. Top with mozzarella and Parmesan.

Heat broiler on high. Broil, watching closely, until cheese is melted and browned, 2 to 3 minutes.

Transfer zucchini to a platter. Top with basil and more red pepper flakes.