Preheat the oven to 400 degrees. Toss the cubed butternut squash with 1 tablespoon olive oil, salt, and pepper on a baking sheet. Roast for 25 minutes until soft.
Bring a large pot of salted water to a boil. Cook the lasagna noodles according to package directions until al dente. Drain and lay them flat on a lightly oiled tray.
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.
Mash the roasted squash in a bowl. Stir in the ricotta cheese, half the mozzarella, and the cooked kale until combined.
Spread 1 cup marinara sauce in the bottom of a 9x13 baking dish. Spoon the squash mixture evenly along each noodle and roll up. Place the rolls seam side down in the dish.
Pour the remaining marinara sauce over the rolls. Sprinkle with the remaining mozzarella and Parmesan cheese. Bake for 20 minutes until the cheese is melted and bubbly.