Using a sharp knife or mandolin very thinly slice the squash into 4mm half moons.
In a large bowl using your hands mix together the squash, halved tomatoes, garlic, tomato puree, fine salt, chopped sage, 4 tbsps of the oil and plenty of pepper. Set aside.
In a separate bowl mix the cream, Parmesan and nutmeg together. Set 80g of the mixture aside to use later.
Cover the bottom of a 28 x23 cm baking dish with a layer of lasagne sheets then follow with a layer of the butternut mixture. Spoon over some of the cream mixture then continue layering the same way until you have run out of pasta, butternut and cream.
Pour the stock evenly over then cover tightly with foil and bake for 50 minutes. Remove from the oven and discard the foil. Spoon over the reserved cream mixture and return to the oven, uncovered, for 10 minutes.
In a small bowl mix the remaining 2 tbsps oil with the remaining 10 sage leaves. Spoon the oil and leaves over the lasagne and return to the oven for 5-6 minutes or until the sage leaves are bright green and crisp, and the lasagne is golden brown.
Leave to rest for 10 minutes, then finish with the 2 tbsps cream , a good drizzle of oil and plenty of grated Parmesan, flaked salt and black pepper.