Preheat the oven to 375°F Oil a 2-quart baking dish or lasagna dish. Bring a large pot of water to a boil.
Place the cottage cheese in a food processor fitted with the steel blade, and blend until smooth. Add 1/2 cup of the tomato sauce, and blend until smooth. Scrape into a bowl.
Wash the spinach, and wilt in a large frying pan over high heat in the water left on the leaves after washing. Transfer to a colander, rinse briefly and squeeze out excess water. Chop fine (by hand or in a food processor), then stir the spinach into the cottage cheese. Season to taste with salt and pepper.
When the water comes to a boil, salt generously and add enough lasagna noodles to cover the surface of the baking dish (for my rectangular dish, that’s three lasagna noodles). Boil just until the pasta is flexible, about two or three minutes for no-boil lasagna. Using tongs, remove the pasta from the water, and drain on a clean dish towel. Spread a thin layer of tomato sauce on the bottom of the baking dish, and top with a layer of noodles. Top the noodles with a third of the cottage cheese mixture. Use a spatula to spread it evenly over the noodles. Top with 1/2 cup of the tomato sauce, and spread in an even layer. Sprinkle on 2 tablespoons of the Parmesan.
Repeat these layers two more times, using up the cottage cheese/spinach mixture but retaining tomato sauce and Parmesan for the top layer. Cook one more batch of lasagna noodles, and top with the remaining tomato sauce and Parmesan. Sprinkle on the bread crumbs, and drizzle on the olive oil. Cover tightly with foil, place in the oven and bake for 30 minutes until bubbling. If you wish to brown the top, uncover and continue to bake until the top just begins to color, about five minutes. Remove from the heat, allow to sit for five to 10 minutes, and serve.