Preheat the oven to 200ºC/gas mark 6. Put half the oil in a large bowl and add the courgettes, aubergine and peppers. Season and toss the vegetables to coat in the oil. Transfer to a large roasting tin and roast for 30 minutes until tender, turning once.
Meanwhile, heat the rest of the olive oil in a large deep saucepan and fry the onion and garlic over a low heat for 10 minutes, stirring frequently, until very soft but not brown. Add the chopped tomatoes and 200ml water. Bring to the boil, then reduce the heat and simmer gently for 10-15 minutes, stirring occasionally until thickened.
Stir the spinach into the hot tomato sauce until just wilted. Remove from the heat and add the roasted vegetables and beans. Season to taste. Reserve half the mixture for later use, or freeze. Reduce the oven temperature to 180ºC/gas mark 4.
To assemble, spread one-quarter of the white lasagne sauce in the base of a 2-litre ovenproof dish. Top with a single layer of lasagne sheets, cutting them to fit if necessary. Spoon over half the vegetable sauce, followed by another quarter of the white sauce. Repeat the layers of lasagne sheets, vegetable sauce and white sauce once more, then top with a final layer of lasagne sheets.
Spread the remaining white sauce over the top of the lasagne sheets. Sprinkle the cheese over the top. Bake in the preheated oven for 35-40 minutes or until golden and bubbling.