Cut the courgettes, the broccoli, the bell peppers and the tomatoes in small pieces.
Sauté them in a Teflon pan with 1 tbs of butter and 1 tbs of olive oil. Season with salt and pepper and set aside.
For the Bechamel sauce: In a pot, melt the butter, add the flour and then pour the milk stirring constantly to avoid lumps. Season with salt and a pinch of nutmeg, then bring to the boil. Cook for only a couple of minutes. Set aside.
Assembly: Grease a Pyrex or a squared oven tray with a little bit of butter. Spoon over the bottom a layer of béchamel sauce.
Create the first layer with the lasagne sheets, cover it with some of the vegetables and sprinkle with grated parmesan.
Repeat this procedure 5 times, altering layers of vegetables, pasta and béchamel. Make sure to leave enough béchamel sauce to cover completely the top layer.
Bake in in a preheated oven at 220 °C for 25-30 minutes.
Leave the Lasagne to rest for 10 minutes out of the oven before serving.