Finely slice the zucchini, add a drizzle of olive oil to a skillet, add the sliced zucchinis, do not overcrowd them, otherwise they won't cook properly; add salt, then sauté them in medium heat until they are golden brown on both sides. You will need to do it in batches, or you can bake them in the oven. Reserve.
Add the mushrooms to the same skillet. Add a drizzle of olive oil if necessary, add the mushrooms, salt, and pepper, and sautéed them until the mushrooms are golden brown. Add the peas and stir for 2 minutes more. Turn off the heat and reserve.
Make the bechamel sauce: Add the vegan butter to a pot, let it melt in medium heat, then add the flour, stir until well combined, and keep stirring for 3 to 4 minutes more. Add the COLD unsweetened plant-based milk little by little until you have no more milk left and your bechamel sauce is silky smooth and lump-free. Since the bechamel cools down, it thickens up so you might need to add a little bit more plant-based milk if it gets too thick. Cover the pot and reserve.
Preheat the oven to 185C (360F). Set aside the nicest looking zucchinis you have previously baked or sautéed for garnishing the top layer of your lasagna. Now, you can assemble your lasagna by spreading some bechamel sauce to the bottom of your baking dish. Then add the lasagna sheets, add some more bechamel sauce, the zucchinis, add the sautéed mushrooms and peas, the vegan cheese, the bechamel, and continue the layering process until your lasagna dish is totally full. Add the cooked spinach and fresh basil leaves along with the mushroom and peas to one layer. Finish with a layer of bechamel sauce and cover with the zucchinis you have set aside for the topping. Add some more bechamel sauce on top of the zucchinis if you like but careful not to completely cover the zucchinis.
IMPORTANT NOTES: 1. I only added the spinach and the fresh basil leaves on one layer, but you can do it on every layer if you prefer, just make sure that the spinach is completely thawed out if frozen and squeezed very well so it doesn’t make your lasagna watery and soupy like. 2. I have also used the vegan cheese in alternated layers so whatever type of vegan cheese you are using, use it sparingly because the bechamel sauce is already “cheesy” enough and to add even more cheese will make all the other flavors disappear; remember, this is a fresh and delicate dish and too much cheese can easily ruin it, so be a little bit careful here. 3. The milk you are using for the bechamel is supposed to be COLD, this will ensure a silky and smooth béchamel sauce.