To make the pumpkin filling:
Heat the oil and butter in a shallow Dutch oven or cast-iron braiser and fry the sage leaves over a gentle heat for about 2 minutes.
Add the chopped onion and minced garlic to the pan and fry very gently for another 10 minutes or so.
Add the pumpkin pieces, turn well in the oniony oil and, after about 5 minutes, add the vermouth (or wine), the water and diced tomatoes. Simmer, covered, for an hour, stirring occasionally so the pumpkin cooks evenly. Taste for seasoning I tend to add quite a bit of salt here and leave to cool.
For the tomato sauce:
Simply pour the tomato sauce and water into a large jug or bowl, and stir in the sugar, salt and pepper, whisking it all together.
To make up the cheese layer:
In a separate bowl beat the goats cheese and ricotta with the eggs, nutmeg, and salt and pepper to taste.
Preheat the oven to 400F, slipping in a large cookie sheet as you do.
To assemble the lasagne, begin by putting 2 cups of the cold tomato sauce in the bottom of a roasting pan (measuring approx.
x 10 x 2 ½ inches).
Then layer with a third of the lasagne sheets, overlapping them well (Italians do it with the pan horizontal but the pasta vertical, if that makes sense, but I dont know that it truly matters). Leave the rest of the tomato sauce aside for the time being.
Layer a third of the pumpkin filling over the lasagne, and dollop on a third of the cheese mixture, coaxing with a rubber spatula. It wont cover completely; think more of spreading blobs about. Then start again with a layer of lasagne, followed by pumpkin, then the cheese. Repeat once more lasagne, pumpkin, and the last of the cheese mixture.
Pour the remaining cold tomato sauce over, letting it sink down and be absorbed in the layers.
Slice and chop the mozzarella and dot over the top.
Bake in the oven, on the cookies sheet, for 1 hour. Once baked, take it out of the oven and let it stand for 15-30 minutes to make cutting and serving easier. (I love when its stood for an hour or so, too.) As you cut and slice, you will notice a shallow tomatoey cheesey pool at the bottom of the pan; bread dunked into this is gorgeous.
Sprinkle the toasted pine nuts over the lasagne, and cut into squares to serve.
