Begin with the eggplant, cut it into evenly shaped pieces. Fry in a frying pan on medium heat with the cooking oil. Fry until you have a nice brown color. Let it cool.
Wash the sweet potato and pick them with a fork. Bake in the microwave for 5-7 minutes on maximum heat. Scrape out the mushy sweet potato and add it into a bowl and mix with a hand blender. If you don't have a hand blender a mixer will do. Add the plant milk, salt, chili and the garlic cloves and mix until you have a nice purée.
Turn the oven on 225ºC/437.00ºF, bring forth a ramekin and start assembling the lasagna. Start with the eggplants, then add the sweet potato mixture, then the spinach and finish off with the cheese. Bake for 10 minutes or until the cheese has melted nicely.