Heat the oven to 200°C/400°. Toss the courgette, pepper, carrot and mushroom with olive oil and salt and pepper. Place on a baking sheet and roast for 25-30 minutes.
Melt the butter in a medium saucepan over a medium heat. Add the flour and cook for about a minute then add the milk a little at a time, whisking well between each addition. Add the nutmeg and plenty of salt and pepper, bring to a gentle simmer and cook until thickened, add the cheddar cheese and stir to melt then remove from the heat.
Spread a spoonful of bechamel in the bottom of a baking dish, top with lasagne sheets followed by another spoonful of bechamel then a third of the vegetables. Repeat another layer of lasagne followed by sauce and vegetables. Repeat one more time then add a final layer of lasagne sheets and pour over the rest of the sauce. Top with the mozzarella and bake for 30-40 minutes until browned and bubbling.
Nutrition information is an estimate and will vary depending on the exact ingredients used.