Heat the oven at 180°C/356°F.
Heat 1 tsp olive oil in a large skillet, add the onions, carrot, celery and two garlic cloves, and cook for 7-10 minutes at low heat , stirring from time to time.
Add the mushrooms and nuts, stir to combine and cook until all the released liquid evaporates.
Add the white wine, stir to combine and cook for 3 more minutes.
Transfer into a food processor bowl, and pulse two or three times, until the mixture ressembles with minced meat.
Put the mixture back in the skillet, add tomato sauce and stir to combine. Cook for 5 minutes over low heat.
Heat the remaining olive oil in the skillet, add one garlic clove, fry it for 30 seconds, just to flavor the oil, then add the spinach and stir to combine.
Cook the spinach until all the liquid evaporates, season with salt and pepper and transfer in a bowl.
Heat the coconut oil in a sauce pan over low heat, add the chickpea flour and stir to combine.
Add the almond milk and vegetable broth, bring to boil and simmer on low heat whisking continuosly until the mixture thickens. Adjust the texture with almond milk. Season with nutmeg.
Grease a baking pan with olive oil, and add layers of lasagna sheets, topped with mushroom ragu, and bechamel sauce.
Repeat with the rest of the composition, and top with a layer of lasagna sheets and cooked spinach.
Beat the eggs, season with salt and pepper and pour on top of the dish.
Cook for 20 minutes.Serve immediately.