Preheat the oven to 190 degrees C. Put the spinach in a large saucepan. Cover and wilt it over a low heat for about 5 minutes, turning it occasionally. Tip the spinach into a colander and allow to drain, but do not squeeze dry. Reserve 2 tablespoons of the juices.
Put the goats cheese and ricotta in a large bowl and mix together. Take out half the mixture and set aside. Add the pesto and reserved spinach juice to the cheese in the bowl then blend until smooth. Stir in the spinach, nutmeg and seasoning to taste.
Lay the lasagne sheets in a roasting tin and pour over enough boiling water to cover. Leave for 5 minutes until softened then carefully drain.
Spread one-third of the spinach mixture over the base of a 25×18×8cm baking dish. Scatter one-third of the tomatoes in an even layer over the spinach mixture. Cover with a layer of pasta, trimming to fit the dish. Add half of the remaining spinach mixture in a thin layer, top with half the remaining tomatoes and cover with pasta as before. Cover with the last of the filling and arrange the remaining pasta sheets over the top.
Whisk the reserved cheese mixture with the eggs, milk and seasoning. Pour over the lasagne then sprinkle with a mixture of the breadcrumbs and Parmesan. Bake for 25 minutes until the topping is lightly set and browned. Serve while hot.