Preheat the oven to 375°F (190°C).
Slice the zucchini lengthwise into approximately 1/8-inch-thick strips using a mandoline, box grater, or sharp knife.
Cover a large baking sheet with two layers of paper towels. Arrange the zucchini slices in a single layer and season them lightly with salt.
Allow the zucchini to stand for 30 minutes so the salt can draw out excess moisture.
Heat the oil in a large skillet over medium-high heat. Add the ground turkey and cook for approximately 5 minutes, stirring frequently and breaking the meat into small pieces as it browns.
Season the turkey with 1 teaspoon oregano, the dried basil, garlic powder, 1/2 teaspoon salt, and freshly ground black pepper. Continue cooking for about 30 seconds so the seasonings become evenly incorporated.
Pour in the tomato sauce and stir in the sugar. Bring the sauce to a boil, then lower the heat and simmer for 5 minutes.
Transfer the finished meat sauce to a medium bowl and reserve it for assembly.
Using the same skillet, add the chopped fresh spinach in batches. Stir continuously as each portion wilts before adding more.
Once all of the spinach has wilted, transfer it to a separate bowl and allow it to cool to room temperature.
Place the cottage cheese in a medium bowl. Add the egg and 1/2 teaspoon dried oregano, then mix thoroughly until evenly combined.
Fold the cooled spinach into the cottage cheese mixture.
Use clean paper towels to gently blot the zucchini slices, removing the moisture that has collected on their surfaces.
Spread a thin portion of the meat sauce across the bottom of a baking dish. Arrange a layer of zucchini slices over the sauce, followed by a portion of the cottage cheese and spinach mixture.
Add some of the shredded mozzarella and continue building layers with the remaining meat sauce, zucchini, cottage cheese mixture, and mozzarella until the ingredients have been used.
Finish with zucchini and a final layer of meat sauce. Sprinkle the remaining mozzarella and grated Parmesan evenly over the top.
Cover the baking dish with aluminum foil and transfer it to the preheated oven. Bake for approximately 30 minutes.
Remove the foil and continue baking for another 10 to 15 minutes, or until the top is lightly browned and the lasagna is heated throughout.
Remove the dish from the oven and allow the lasagna to rest for several minutes before cutting into portions and serving.