Preheat oven to 375 degrees F.
Heat a large oven-safe skillet over medium heat. Add 1 tablespoon olive oil, then add in squash with 1/4 teaspoon salt, the pepper and the nutmeg. Stir to coat well and add in 1/3 cup stock. Cover and cook until softened, about 10-12 minutes. Once soft, remove squash with a large spoon (and any extra stock, though most of it will cook away) and place in a bowl. Mash well with a potato mashed or fork.
At this time, prepare the water for the pasta and boil according to directions, shaving a minute or 2 off the time since you will cook the pasta more in the oven. While water is boil/pasta is cooking, continue with the rest of the recipe.
With the skillet still hot, add in the other tablespoon of olive oil, then toss in onion with 1/4 teaspoon salt. Still well to coat, cooking for 2-3 minutes until slightly soft, then add in ground chicken with remaining salt to season. Break apart the chicken using a wooden spoon, continuing to do so as it cooks so it is in small bits. Cook until golden and cooked through, about 5-6 minutes. Once cooked, remove chicken and onions (if a few remain it’s fine) and place in a smaller bowl.
With the skillet still hot, add in butter and once it sizzles, whisk in flour. Cook for 1-2 minutes until golden and nutty, then add in milk, stirring constantly. Continue to stir and one it begins to thicken and bubble on the sides, whisk in mascarpone and parmesan with a pinch of nutmeg, turning the heat down to low. At this time, add the mashed butternut squash back into the milk mixture and whisk to combine. It will probably be very, very thick so add in additional stock, beginning with 1/4 cup, stirring until it is just a bit thinner. Note: it will still be pretty thick! Use your judgement and add a little more if needed. You can also taste the “sauce” here and season more if desired.
Add in the chicken/onion mixture and slowly add the lasagna noodles, strategically placing them if needed. I took a few seconds and pushed mine around/separated them just to spread them throughout the skillet. Top with sliced mozzarella, panko and sage leaves. Bake for 20-25 minutes, or until cheese is golden. Serve immediately. This reheats fairly well, but you must add some liquid and do some stirring as you go!