Preheat oven to 425° and position racks in upper and lower thirds of oven.
Slice zucchini lengthwise to get 24 total strips, about ⅛ inch thick each. Use a mandolin slicer to get them ultra-thin, if possible.
Toss the zucchini in ¼ tsp olive oil, and kosher salt and pepper to taste in a large bowl. Arrange the zucchini in a singel layer on 2 rimmed baking sheets.
Bake the zucchini, turning once, until tender, about 10 minutes total.
Meanwhile, combine 2 tbsp. mozz and 1 tbsp. parm in a small bowl. Mix egg, ricotta or cottage cheese, spinach, garlic, and the remaining 6 tbsp. mozz and 2 tbsp. parm and ¼ tsp. ground black pepper and ⅛ kosher salt in a medium bowl.
Spread ¼ cup marinara in an 8-inch square baking dish. Place 1 tbsp. of the ricotta (or cottage cheese) mix near the bottom of the strip of zucchini. Roll it up and place, seam-side down, in the baking dish. Repeat with the remaining zucchini and filling. Top the rolls with the remaining ½ cup marinara sauce and sprinkle with the reserved cheese mixture. Sprinkle Italian seasoning on top.
Bake the zucchini until the cheese is bubbly, about 20 minutes. Sprinkle with more Italian seasoning, if desired, right before serving.