Preheat the oven to 500 degrees . Line 2 baking sheets with parchment paper. Place the eggplant and zucchini in two large bowls and season with salt; let stand for 40 minutes. Rinse the vegetables and pat dry. Arrange in a single layer on the prepared pans and toss with 3 tablespoons olive oil. Roast until golden, about 20 minutes. Transfer to a 9-by-11-inch baking dish. Lower the oven temperature to 350 degrees .
Meanwhile, in a large skillet, heat the remaining 1 tablespoon olive oil over medium heat. Add the scallions and garlic and cook, stirring, for 2 minutes; add the ground beef and cook, breaking up the meat, for about 4 minutes. Add the tomatoes and simmer until thickened, about 10 minutes; season with salt and pepper. Spoon the meat sauce over the eggplant and zucchini. Top with half of the gruyere.
Using a food processor, puree the cottage cheese. Spoon the puree onto the moussaka, top with the remaining gruyere and bake for 17 minutes. Transfer to the broiler and cook for 3 minutes. Let stand for 15 minutes before slicing.