First, chop the vegetables (pepper, onion, courgette, mushrooms, and tomatoes). I cut mine fairly small, but you can make a chunkier lasagne if you prefer.
Heat the oil in a large frying pan, and add the chopped onion, courgette, mushrooms, garlic, and the frozen sweetcorn. Cook over a medium heat for around 15 minutes, stirring regularly, until all the vegetables are fairly soft. Add the cherry tomatoes, dried herbs, and some salt and pepper, and cook for a minute or two more.
Meanwhile, prepare the white sauce. Melt the butter in a saucepan over a fairly low heat, and add the flour. Mix to form a paste, and cook for a minute or so. Then add the milk a little at a time, stirring the mixture until it's smooth and well-combined each time before adding more milk.
When you've used all the milk, and the sauce is smooth, add about two thirds of the grated cheese. Mix well, and cook for a minute or two until the cheese has melted into the sauce.
To assemble the lasagne, begin by adding about 1 tbsp of the cheese sauce to the bottom of a baking dish (mine measured 8 x 8 inches), and spreading it around. This just helps to stop the lasagne sticking to the dish, and gives some moisture to cook the bottom layer of pasta.
On top of the smear of sauce, add a layer of lasagne sheets, breaking them to roughly fit the shape of the dish (it doesn't need to be exact!). Top the pasta with about a third of the vegetable mixture, and another couple of spoonfuls of sauce. Repeat the pasta-veg-sauce layers about two more times, finishing with all the remaining cheese sauce. Make sure there's enough sauce on the top of the lasagne to completely cover the pasta, as any uncovered pasta will burn and won't soften properly.
Top the lasagne with the remaining grated cheese and a few slices of tomato. Cover the dish, and bake at 190°C (Gas Mark 5 / 375°F) for around 50 minutes, until the lasagne is tender. Uncover the dish for the last 15 minutes or so of the cooking time, to help the topping crisp up.
Leave to stand for about 5-10 minutes before serving, as this will help you to cut neat slices of lasagne.