Boil the potatoes for about 10-12 minutes or until soft when pierced with a fork. Before the end of the cooking time add the green beans and cook for 2-3 minutes.
Place a medium sized saucepan over a medium high heat and add in the butter. When it’s completely melted and foaming add in the flour and whisk until you are left with a roux (a thick, smooth paste). Cook for 2 minutes before whisking in the milk gradually. Continue to whisk and cook until the sauce holds a figure of eight when swirled with the whisk. Season with sea salt and ground black pepper and stir in the nutmeg. Remove from the heat and stir through the pesto.
Preheat the oven to 200˚C/400°F/Gas Mark 6. Spread a little of the pesto sauce across the base of medium sized roasting tin. Lay sheets of the pasta across the base top with the sauce, green beans, slices of potatoes and a generous sprinkle of Parmesan. Repeat the process layering up the lasagne with the remaining ingredients until you are left with a final layer of pasta sheets.
Pour over the remaining sauce, sprinkle with Parmesan and dot with a little butter. Place in the oven to bake for 25 minutes until bubbling and golden. Serve straight away with a fresh salad.