Heat your oven to 400F (200C).
Make the bechamel sauce. Place a saucepan on a medium heat and add the butter.
Stir in the flour when the butter has melted.
Add the milk gradually and stir continuously until a thick sauce is formed.
Stir in the ground nutmeg, black pepper, and salt and leave the pan on its lowest heat while you prepare the green veg lasagna filling.
Place a Dutch Oven or large frying pan on a medium to high heat and add the olive oil.
Add the broccoli and sauté for 3 minutes then add the vegetable stock and cook for 2-3 more minutes.
Add the frozen peas to and simmer for 2 minutes.
Add the spinach to the pan, stir it in and leave on a medium heat until wilted. You might need to do this in batches.
Stir in the green pesto and remove the pan from the heat. (note 3)
Assemble the lasagna. Spoon 1 third of the green veg pesto mixture into the bottom of your baking dish, then add the bechamel sauce and top with a layer of fresh lasagna sheets. Repeat for 2 more layers.
Spread any remaining bechamel sauce on the top layer of lasagna sheets and sprinkle grated mozzarella and Parmesan on top.
Place the lasagne towards the top of your oven for 15-20 minutes until the top is brown and you can see the sauce bubbling around the edges.
Leave to cool for 10 minutes before serving.