In a bowl, stir together pumpkin puree, sliced sage, nutmeg, 0.5 tsp salt, and 0.25 tsp black pepper. Set aside to let the flavors meld.

Heat olive oil in a large skillet over medium-high heat. Add garlic and cook 30 seconds until fragrant. Add spinach in batches, turning with tongs, until completely wilted and any liquid evaporates, about 4 minutes. Transfer to a colander, press out excess moisture, and roughly chop.

In a medium saucepan, melt butter over medium heat. Whisk in flour and cook 1 minute until foamy and pale golden. Slowly pour in warm milk while whisking constantly. Continue cooking, whisking often, until thickened enough to coat the back of a spoon, 6 to 8 minutes. Remove from heat and stir in 0.5 cup parmesan and 0.5 tsp salt.

Preheat oven to 375 degrees F. Spread 0.5 cup bechamel in the bottom of a 9x13 inch baking dish. Add a layer of noodles, breaking to fit as needed. Spread half the pumpkin mixture, then half the spinach. Dollop half the ricotta in spoonfuls and spread gently. Pour 1 cup bechamel over top and sprinkle with 0.5 cup mozzarella. Repeat layers once more. Finish with a final layer of noodles, remaining bechamel, and remaining mozzarella and parmesan.

Cover tightly with foil and bake 30 minutes. Remove foil and bake until top is spotty golden and edges are bubbling, 15 to 20 minutes more. Let rest 15 minutes before slicing so the layers set.