Cook lasagne sheets in a large pot of lightly salted, boiling water for 10 minutes, or until al dente. Rinse with cool water, drain and set aside.
Heat oil in a large frying pan over medium heat. Cook the chopped onions, mushrooms, garlic and courgette in the oil until soft. Stir in passata, oregano, brown sugar and salt. Reduce heat to low, and simmer for 15 minutes.
Meanwhile, microwave frozen spinach until cooked. Cool, and then squeeze out excess water. Drain cottage cheese. Using a mixer, blend spinach, cottage cheese, eggs and 2 tablespoons basil until smooth. In a separate bowl, combine shredded mozzarella cheese and grated Parmesan cheese.
Preheat oven to 180 C / Gas 4. Spread a third of sauce in the bottom of a baking dish. Layer a third of the lasagne sheets, a third of the cottage cheese/spinach mixture, a third of tomato-vegetable sauce mixture and a third cheese mixture. Repeat layers with remaining ingredients. Sprinkle top with remaining 1 tablespoon of dried basil.
Bake in preheated oven for 60 minutes. Let stand for 10 minutes before serving.
Parmesan cheese is not truly vegetarian, as it contains animal rennet. To make this dish 100% vegetarian, omit the cheese or find a suitable vegetarian substitute made without animal rennet. In supermarkets look for the 'parmesan style hard cheeses' which are suitable for vegetarians.