Preheat the oven to 350 degrees F.
Heat 1 tbsp of oil in a skillet. Add half the garlic and as it begins to turn golden, add the oregano and the fresh mushrooms. Season to taste with salt and ground black pepper. Saute, stirring frequently, for five minutes or until the mushrooms start to brown. Drain the reconstituted mushrooms and add to the skillet. Reserve the mushroom stock. Add the wine.
Continue cooking for another five minutes until the wine has evaporated, then add the leeks. Continue cooking another five minutes or until the leeks are just tender. Turn off the heat and set aside.
Make the bechamel. In a saucepan, heat the remaining oil. Add the shallot and the remaining garlic. Season with salt and pepper and cook until the shallots start to turn translucent. Add the flour and cook, stirring frequently, over medium heat, until the flour begins to brown.
Slowly, stir in the cashew milk, using a whisk to beat out any lumps of flour, until you have smooth sauce. Add the reserved mushroom sauce. Add nutmeg, check seasoning and add more salt and ground black pepper if needed.
Let the sauce come to a boil and thicken. It should be thick enough to coat the back of a spoon. Turn off the heat. Reserve 1 1/2 cups of the sauce and add the rest of it to the mushroom and leek mixture and stir well.
Coat the bottom of a 12 X 8 inch baking pan with the reserved bechamel sauce. Layer lasagna noodles side by side on top. In the pan I used, three noodles fitted side by side in each layer.
Pour one-third of the mushroom-leek mixture on top of the lasagna noodles in an even layer. Sprinkle on one-third of the vegan mozzarella
Arrange three more noodles on top and again layer on one-third of the mushrooms and leeks and the mozzarella. Repeat one more time, and finish off by layering mushrooms and leeks, mozzarella, and the vegan parmesan on the top layer.
Cover the lasagna pan with tinfoil and bake in the preheated oven for 45 minutes. After 45 minutes, take off the foil and let the lasagna cook another 15 minutes.
Let the lasagna stand 10 minutes. Garnish with parsley before serving.