Begin by preparing your vegetables. Heat the oil in a frying pan, and add the diced onion, asparagus and sugarsnap peas. Cook over a fairly low heat for 5 minutes, stirring regularly, and then add the garlic and mushrooms. Cook for a further 5 minutes, until the mushrooms have cooked down and the mixture is fairly dry. Remove from the heat, and add the tomatoes and sweetcorn. Set aside.
Next, make the creamy sauce. Melt the butter in a saucepan, and add the flour. Whisking constantly, cook over a very low heat for a minute or two, and then add the milk a little at a time, whisking until smooth each time before adding another dash. Add the nutmeg and plenty of seasoning, along with the grated cheddar. Whisk for one more minute until the cheese has melted into the sauce, and then remove from the heat.
Heat the oven to 190°C (Gas Mark 5 / 375°F).
Now you can begin to construct the lasagne. Begin with about a tablespoon of sauce, spread out over the bottom of a baking dish (mine measured around 8 x 6 inches). Add a layer of lasagne sheets, breaking them into pieces so that they cover the bottom of the dish in a single layer.
From here on, it doesn't matter too much how you create your layers, but here's how I made mine: 1/3 of the vegetable mixture; 1/3 of the sauce; layer of lasagne; another 1/3 of the vegetables; another 1/3 of the sauce; another layer of lasagne; remaining vegetables; remaining sauce. Make sure any corners of lasagne are covered in at least a little bit of the sauce to stop them from burning.
Once you've used up all of your vegetables and sauce, top the dish with the grated mozzarella and slices of tomato. Bake for around 40 minutes, or until the cheese is crispy and golden brown and the lasagne is tender. If the cheese is browning too quickly, just cover the dish loosely with foil and return to the oven until the pasta is cooked.
Leave to stand for 5-10 minutes before serving.