Preheat the oven to 400°F/200°C.
Peel the butternut squash with a vegetable peeler, then cut just above the bulb. Slice that long piece into four pieces.
Place each of the four pieces of butternut squash with the flat side down and safely run them through a mandoline slicer until you're left with a pile of thin butternut squash noodles. Side note: Mandolines are very sharp, so either use a safety guard or safety gloves to ensure you keep all your fingertips. Heat a tablespoon of olive oil in a large skillet over medium heat. Once hot, cook the onion and garlic until the onion is translucent, about 3-5 minutes, stirring occasionally. Season with salt and pepper.
Add the meat and cook until browned, then add in the fresh spinach. It'll look like a lot at first, but it'll drastically reduce in size once cooked. Remove from the heat, and add the tomato sauce (minus the 1 reserved cup).
Layer the lasagna by adding a little bit of the reserved sauce to the bottom of a 9x13 baking dish, followed by a layer of butternut squash noodles. Add a few spoonfuls of the meat and spinach mixture on top of the butternut squash, followed by ricotta dollops (or spread them out) to only one of the meat and spinach layers, reserving the rest of the ricotta for the top. Repeat this process with the noodles and meat sauce until you use them up.
Spread the reserved tomato sauce and the remainder of the ricotta cheese over the top layer of the butternut squash sheets.
Bake uncovered for 1 hour. Allow to cool to room temperature for a few minutes before serving.