Preheat the oven to 350°F.
Slice each zucchini lengthwise into eight ⅛-inch-wide strips, totaling 16 strips. Use a mandoline for ease, or carefully cut by hand with a sharp knife.
Lightly spray two large baking sheets with cooking spray. Arrange the zucchini slices in a single layer on the sheets, allowing slight overlap if necessary. Season with salt and pepper.
Bake for 15 to 20 minutes, flipping the zucchini slices halfway through, until softened and pliable. Remove from the oven and let cool for a few minutes until handleable.
While the zucchini bakes, combine the spinach, ricotta cheese, 1 cup mozzarella cheese, ¼ cup Parmesan cheese, egg, dried basil, nutmeg, salt, and pepper; mix until well-combined.
Spread 1 cup of marinara sauce in a 9x13-inch baking dish.
Place one zucchini strip on your work surface. Spoon a portion of the spinach and cheese mixture onto the end closest to you. Roll up the strip and place it seam-side down in the baking dish. Repeat with the remaining zucchini and filling, ensuring even portions.
Top the roll-ups with the remaining marinara sauce, then sprinkle with the remaining ½ cup mozzarella cheese and ¼ cup Parmesan cheese.
Bake, uncovered, for 45 minutes, or until the filling is heated through and the sauce is bubbly in the center and around the edges. Continue baking until bubbly in the center to allow excess liquid to evaporate.
Remove the baking dish from the oven and let the roll-ups rest for 10 minutes before serving.
Sprinkle with chopped fresh basil, if desired.