Heat 1 tablespoon of the olive oil over medium heat. Add the onion and stir to coat in the oil. Cook until the onion softens and is translucent, about 7 minutes, then add the garlic and cook until fragrant, about 3 to 5 minutes more. Add the ground beef and lamb, breaking apart the meat with the end of your stirring spoon as it cooks. Once it's nearly cooked through, use a spoon or small ladle to remove and discard the excess fat pooling at the bottom of the pan.
Add the tomato paste, water, 1 teaspoon of the salt, black pepper, and cinnamon. Mix well, lower the heat, and allow to simmer uncovered for about 15 minutes. Remove the pan from the heat, empty the contents into a large bowl, and allow the mixture to cool until warm (not hot). Stir in the whisked egg and set aside.
Peel the butternut squash and cut the neck into 16 *very* thin slices (like, as thin as you possibly can). Cut the remainder of the squash in half lengthwise and scoop out and discard the seeds. Cut the squash into 1/4-inch thick slices length-wise.
Preheat the oven to 350 degrees Fahrenheit. Strain the cashews and discard the soaking liquid. Puree together the milk and the strained cashews in a blender or food processor at high speed until silky smooth. Set aside.
Melt the butter in a medium sized pot over low heat. Add the flour to the butter and whisk until it forms a paste. Add the cashew milk mixture, 1/2 cup at a time, whisking well after each addition. Stir in the seasonings and allow to cook uncovered for 10 minutes, stirring every few minutes.
Place the whisked egg yolks in a small bowl and add 1/2 cup of the bechamel sauce to the bowl, whisking constantly. Add another 1/2 cup of the bechamel sauce to the bowl and mix well. Pour the egg yolk mixture back into the pan and whisk until completely blended. Continue cooking for about 3 minutes, stirring constantly. Remove the pan from the heat and set it aside.
Mix together the thyme, rubbed sage, and remaining 3/4 teaspoon salt in a small bowl and set aside.
Grease a casserole pan measuring about 9 x 13 inches and at least 2 inches deep. Cut the lengthwise slices of butternut squash to fill the bottom of the pan in a single even layer (you can look at the photo example below for reference). We'll be making one more layer of the lengthwise slices later on, so make sure you're only using about half of them for this layer.
Once you've created a single layer of butternut squash slices on the bottom of the pan, sprinkle some of the spice mixture and the cheese over it. Pour the lamb and beef mixture over the squash layer, spreading it out an even layer and pressing it down with the back of your spatula or spoon to help flatten and even it. Sprinkle with some of the cheese and spice mixture.
Create another even layer of the lengthwise-slices of butternut squash and more grated cheese and ground sage. Pour the bechamel sauce over it, and use a rubber spatula to spread it in an even layer.
Then lightly brush the butternut rounds with the remaining tablespoon of olive oil and arrange them in 4 rows of 4, with the edges slightly overlapping in each row. Sprinkle the remaining cheese and spice mixture over the top. Place the pan in the oven and bake until the squash rounds wrinkle around the edges and the top of the bechamel sauce begins to brown, about 1 hour. Allow to cool for 30 minutes before slicing and serving.