Preheat the oven to 400°F. Spread the cubed butternut squash on a baking sheet, toss with a pinch of the salt, and roast for 25 minutes until soft and lightly browned. Set aside.
Bring a large pot of salted water to a boil. Cook the lasagna noodles according to package directions until al dente. Drain and set aside.
In a large skillet over medium heat, melt the butter. Add the sage leaves and cook until the butter turns golden brown and smells nutty, about 4 minutes. Stir in the garlic and cook for 30 seconds more. Remove from heat and discard the sage leaves.
Add the chopped kale to the brown butter in the skillet. Cook over medium heat until the kale wilts, about 3 minutes. Season with the remaining salt and pepper.
In a 9x9 inch baking dish, spread a thin layer of the brown butter mixture. Add a layer of noodles, then half the roasted squash, half the kale, dollops of ricotta, and a sprinkle of mozzarella. Repeat the layers once more, finishing with the remaining noodles, mozzarella, and Parmesan on top.
Cover with foil and bake for 20 minutes. Remove the foil and bake for another 10 minutes until the cheese is bubbly and golden.