Preheat the oven to175C/346F.
Heat the olive oil into a cast iron skillet and add the mushroom slices.
Cook over medium heat,stirring frequently, until all the liquids evaporated. Transfer in a bowl and set aside.
Add the diced carrot and garlic into the skillet, and cook for 5 minutes over medium heat,stirring frequently.
Add the rest of the sauce ingredients, mix to combine and bring to boil.
Turn the heat to low, lid the skillet and simmer for 15 minutes.
Add the cashew cream ingredients into the blender and process to obtain a smooth, creamy liquid. Add more almond milk to obtain the desired consistency.
Spread 3 tbsp of the tomato sauce on the bottom of a baking pan (I used a 9x13 one).
Arrange a layer of lasagna sheets, top them with a layer of spinach and mushroom slices, drizzle tomato sauce and cashew cream and top with another layer of lasagna pasta.
Continue until all ingredients are layered, and top everything with a layer of lasagna sheet.
Drizzle cashew sauce on top, drizzle with olive oil and bake for 40 minutes, until the pasta is cooked.
Cut into squares and serve.