Place a aluminum-lined baking sheet in the oven and preheat to 400°F (200°C) conventional, or 375°F (185°C) fan.
Prepare the onions:Separate the sliced onion layers. Melt the butter in a sauté pan over low heat, then add the onions and increase to medium. Cook for 5 minutes, stirring often.Reduce heat to medium-low, season with salt, and add the cider. Simmer gently for about 1 hour, stirring occasionally. Add a splash more cider and lower the heat if the onions stick or brown. The onions should be pale and tender.
While the onions are braising, prepare the butternut squash:Drizzle the cut sides of the squash with olive oil and rub to coat. Carefully remove the pre-heated baking sheet and place the squash cut-side down. Prick the skin a few times with a knife.Cook in the middle of the oven for about 45 minutes, until the skin is blistered and the flesh is very tender. Let cool slightly, then discard the skin and transfer the flesh to a bowl. Mash until smooth. Mix in the ricotta, thyme, salt, and pepper until fully combined.
While the butternut is roasting, make the béchamel:Melt the butter in a pot over medium-low heat until foaming (do not brown). Add the flour and whisk until smooth. Cook for 3–5 minutes, whisking constantly, until pale, silky, and lightly toasty.Remove from heat. Add a small splash of milk and whisk until smooth, then add the remaining milk in two additions, whisking well after each.Return to medium-low heat and simmer gently for about 10 minutes, whisking often, until thick enough to coat the back of a spoon. Remove from heat and season with salt and a pinch of nutmeg.Press plastic wrap directly onto the surface and reserve.
Assemble and cook:Spread a very thin layer of béchamel in the bottom of the baking dish. Repeat the following layers 3 times: lasagna sheets → butternut squash purée → onions → taleggio → béchamel. Finish with a generous layer of grated parmesan.Cover tightly with aluminum foil and cook in the middle of the oven for 30 minutes. Remove the foil and bake for 15 minutes more, until bubbling. Broil briefly, watching closely, until golden.