Preheat the oven to 200C/180C fan/400F/gas 6, slipping in a baking sheet as you do.
To make the pumpkin filling: heat the oil and butter in a shallow casserole dish or roasting tin 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 then add the vermouth (or wine), the water and chopped tomatoes. Roast in a pre-heated oven for 30 to 45 minutes, stirring occasionally. Taste for seasoning – I tend to add quite a bit of salt here – and leave to cool.
For the tomato sauce: simply pour the chopped tomatoes 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 goat’s cheese, cream cheese, Cheddar and ricotta with the eggs, nutmeg, and salt and pepper to taste.
To assemble the lasagne, begin by putting 500ml of the cold tomato sauce in the bottom of a roasting tin (measuring approx 36cm x 26cm x 6cm). Then layer with a third of the lasagne sheets, overlapping them well. 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 won’t 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 balls and dot over the top.
Cook in the oven, on the baking sheet, for 1 hour. Once cooked, take out of the oven and let it stand for 15-30 minutes to make cutting and serving easier. (I love this when it’s been standing for an hour or so, too.) As you cut and slice, you will notice a shallow tomatoey cheesy pool at the bottom of the tin; bread dunked into this is gorgeous.
Sprinkle the toasted pine nuts over the lasagne, and cut into squares to serve.
MAKE AHEAD TIP Up to 2 days ahead, make the pumpkin filling, leave to cool and keep, covered, in the fridge. Make the cheese layer and keep, covered, in the fridge. When ready to use, assemble the lasagne and cook as directed.
FREEZE AHEAD TIP Cook, cool and freeze the cooked pumpkin for up to 1 week. Thaw overnight in the fridge. When ready to use, assemble the lasagne and cook as directed.