Preheat oven to 375 degrees. In a large skillet, heat 1 tablespoon of olive oil. Add turkey sausage and using a wooden spoon break it up as it cooks, ~8 minutes. Transfer cooked sausage to a bowl. Place pan back on the heat, add another ½ tablespoon olive oil, then add chopped onion, eggplant, kale and garlic. Cook for ~7-8 minutes, stirring occasionally. Add sausage back into the pan. Season lightly with a pinch of salt, pepper and ½ teaspoon dried sage. Set aside.
In a large pot over medium heat, melt butter, then sprinkle flour on top and whisk together. Slowly add milk, stirring constantly until little bubbles form and mixture thickens (this will take about 4-5 minutes after those little bubbles form). Add puree pumpkin to the milk mixture and whisk well until combined. Add ½ teaspoon salt, ½ teaspoon pepper, pinch of nutmeg and ½ teaspoon dried sage.
To assemble, use a 13×9 lasagna pan, mix the two cheeses together in a small bowl. Spread ~1 cup of pumpkin sauce on the bottom. Add 3 no-boil lasagna noodles. Top with 1½ to 2 cups of meat/veggie mixture, then ~1 to 1½ cup of sauce and a handful of the cheese. Repeat layers 2 times, ending with a layer of the lasagna noodles, topped with the remaining sauce and the remaining cheese. Cover with tented foil and bake for 45 minutes. Remove foil and bake for an additional 10 minutes. Serve with additional grated Parmigiano-Reggiano before serving.