Heat the oven to 200C/180C fan/gas 6. Tip the squash and garlic into a large roasting tin or dish (you can use the same one to assemble the lasagne to save on washing-up – ours was 35 x 40cm and 5cm deep). Tear over 4-5 sage leaves, drizzle with the oil and season well, then toss to coat. Roast for 40-50 mins, moving the squash around once or twice, until soft and caramelised. Squeeze the garlic from the skins and mash with the squash, leaving a few chunky bits for texture.
Meanwhile, make the white sauce. Melt the butter in a large saucepan, and stir in the flour to make a sandy paste. Splash a little milk into the pan, stirring continuously to prevent lumps. Keep adding more milk, a little at a time, until the paste thins to a smooth, creamy sauce and the milk has all been used. Simmer for 1 min more. Stir in the mascarpone and half the parmesan. Season well and grate in a generous amount of nutmeg.
Tip the spinach into a colander and pour over a kettleful of boiling water to wilt (do this in batches). Once cool enough to handle, squeeze the spinach over the colander to remove the water, then season and roughly chop.
Remove half of the crushed garlicky squash from the roasting tin and set aside on a plate. Spread the remaining squash out over the base of the tin or dish you intend to serve the lasagne in. Ladle over about a quarter of the sauce, then top with a single layer of lasagne sheets, snapping them to fill any gaps. Make an even layer of spinach on top of the pasta, and top with another quarter of the sauce, more pasta, squash, sauce, pasta and finally the remaining white sauce.
Scatter over the remaining parmesan, the mozzarella and pine nuts. If the oven is off, heat to 200C/180C fan/gas 6 and cook the lasagne for 30 mins. Rub a little extra oil over 5 or 6 sage leaves, place them on top of the lasagne and return to the oven for another 15-20 mins until golden and bubbling. Leave to cool for 5 mins before serving.