Position oven racks in top third and lower third; preheat to 450°F. Coat 2 large rimmed nonstick baking sheets with cooking spray.
Stir Parmesan, oil, Italian seasoning, garlic powder and crushed red pepper together in a small bowl until the cheese is well coated.
Cut cabbage lengthwise into 6 to 8 (3/4-inch) slices; cut each slice in half lengthwise (leave smaller end pieces whole, about 12 slices total). Evenly spread Parmesan mixture on 1 side of each cabbage slice (about 1 tablespoon), pressing to adhere. Arrange the slices, cheese-side down, along the edges of the prepared baking sheets, about 3 inches apart.
Bake until the cabbage is tender-crisp and the Parmesan creates a golden-brown crust on the bottom, about 12 minutes, rotating the pans between the top and bottom racks and from front to back halfway through. Remove from oven; let stand for 3 minutes. Using a spatula, turn the cabbage over, cheese-side up; return to oven and bake until tender, 4 to 5 minutes.
Meanwhile, stir parsley, basil (if using), lemon zest, grated garlic and salt together in a small bowl. Let the cabbage stand for 5 minutes before topping with the gremolata and serving.