Heat the oven to 375°F.

Make the béchamel: In a medium saucepan, heat butter on medium until browned and fragrant, swirling often, 3 to 5 minutes. Be careful not to burn butter. Add flour, cook 1 minute, whisking constantly. While whisking, slowly add the hot milk. Cook 4 to 6 minutes or until slightly thickened, whisking frequently. Stir in the pumpkin, big pinch of salt, several cracks of pepper, and nutmeg. Simmer for another minute or two, until sauce is thick enough to coat the back of a spoon. Taste and adjust seasoning as necessary- it should be well-seasoned and not bland. Set aside.

Heat a large skillet over medium. Add olive oil and chopped onion; season with salt. Cook, stirring occasionally, until the onion is softened and translucent, 8-10 minutes. Add garlic and red pepper flakes and cook until fragrant, about 1 minute. Working in batches, place the spinach in the pan, adding more as it wilts. Add a drizzle of olive oil between batches if the pan starts to look dry. Taste and add salt if needed. If there appears to be a lot of liquid in the pan after the spinach is cooked, drain it in a colander, squeezing out excess liquid.

To assemble the lasagna: add ⅓ of the béchamel to the bottom of a 9x13 pan. Place lasagna noodles on top. They should be snug but not overlapping (slight overlapping is okay). Add half of the spinach mixture on top of the noodles. Cover with ⅓ of each type of cheese. Pour another ⅓ of the béchamel over the cheeses. Add another layer of noodles, remaining spinach mixture, and another ⅓ of each cheese. Top with last layer of noodles. Pour remaining béchamel over and top with remaining cheese.

Cover and bake 30 minutes. Remove cover and bake 15 minutes longer or until edges are bubbly and golden brown.

Remove from oven and let rest 15 minutes. Top with fried sage leaves before serving.