Trim the ends of the zucchinis and slice them lengthwise into thin, uniform 1/8-inch thick ribbons using a mandoline slicer.
Arrange the slices in a single layer on paper towels, sprinkle lightly with salt, and let sweat for 10-15 minutes. Firmly blot away all surfaced water droplets with a clean towel.
Preheat oven to 375°F (190°C). Lay blotted zucchini on a parchment-lined baking sheet, brush lightly with olive oil, and pre-bake for 5-7 minutes until flexible but not mushy. Remove and cool.
In a medium mixing bowl, vigorously stir together the ricotta cheese, 1/2 cup of shredded mozzarella, Parmesan, egg, minced garlic, dried Italian seasoning, salt, and pepper until completely smooth.
Spread 1 cup of the marinara sauce evenly across the bottom of an 8x11-inch baking dish.
Lay a zucchini slice flat, spoon 1 generous tablespoon of cheese filling onto one end, and roll up snugly. Place the roll seam-side down into the baking dish on top of the sauce. Repeat for all remaining slices.
Spoon the remaining 1/2 cup of marinara sauce in small dollops over the centers of the rolls. Top evenly with the remaining 1/2 cup of mozzarella and a pinch of extra Parmesan.
Bake uncovered for 25-30 minutes until the sauce is bubbling vigorously and the cheese top is melted and golden-brown. Let rest for 5 minutes, garnish with fresh parsley and basil, and serve hot.