Preheat the oven to 375°F. Bring a large pot of salted water to a boil and cook the lasagna noodles until just tender. Drain and set aside.
Toss the cubed butternut squash with 1 tablespoon olive oil, salt, pepper, and the dried sage. Spread on a baking sheet and roast for 25 minutes until soft. Mash lightly with a fork once cooled.
Heat the remaining tablespoon of olive oil in a skillet over medium heat. Add the minced garlic and cook for 1 minute. Add the chopped kale and cook until wilted, about 4 minutes. Season with salt and pepper.
In a bowl, stir the ricotta with half the grated parmesan and a pinch of salt.
Spread a thin layer of mashed squash in the bottom of a 9x9 baking dish. Add a layer of noodles, then half the ricotta mixture, half the kale, and a sprinkle of mozzarella. Repeat the layers once more, ending with noodles on top.
Spread the remaining squash over the top noodles. Scatter the rest of the mozzarella and parmesan across the surface.
Cover with foil and bake for 25 minutes. Remove the foil and bake 10 minutes more until the cheese is lightly browned. Let the lasagna rest 5 minutes before slicing.