Melt the butter. Then stir in the flour and pour in the milk gradually. Stir until the sauce thickens and add ground nutmeg, ground black pepper, and a little salt.
Sauté the broccoli for a few minutes, add the vegetable stock and simmer until the broccoli is tender. Add the peas, stir in the spinach and continue to cook until wilted. Then stir in the pesto.
Spoon one-third of the green veg mixture into your baking dish. Then spread on a quarter of the béchamel sauce. Place a layer of lasagne sheets on top and continue for two more layers.
Bake for 15-20 minutes until the top begins to brown and you can see the sauce bubbling around the edges. Leave to cool for 10 minutes before serving.