Make the pesto cashew cream cubes: In a blender, combine the cashews, olive oil, basil, nutritional yeast, lemon juice, salt, onion powder, garlic powder, pepper, and garlic. Blend until smooth.
Grease an ice cube tray with nonstick spray. Spoon the pesto into the cups in the tray. Cover with plastic wrap and freeze until the cubes are firm, at least 4 hours or up to 3 days.
Make the lasagna: Heat a large pot over medium-high heat. Add ¼ cup (60 ml) of olive oil to the pot and swirl to evenly coat. Add the eggplant and cook, stirring occasionally, until very soft and caramelized, 30 minutes. Transfer the eggplant to a bowl and set aside.
Add the remaining 2 tablespoons of olive oil to the pot. Then, add the carrot, celery, and onion, and cook, stirring, until softened and starting to caramelize, 10 minutes. Season with salt and pepper.
Add the wine and cook, stirring, until completely evaporated, about 4 minutes.
Add the tomato paste and garlic, and cook, stirring, until lightly caramelized, about 2 minutes over medium heat.
Stir in the reserved eggplant, vegetable stock, and crushed tomatoes and stir to combine.
Remove the pesto cubes from the ice cube tray, and immediately distribute the frozen pesto cubes throughout the eggplant sauce.
Using your fingers or a pair of tongs, insert the noodle pieces vertically in the sauce around the pot. Cover the pot.
Reduce the heat to medium-low, and cook for 18 minutes, then uncover the pot and use a spatula to push down the exposed noodles so they are covered in sauce. Cover and cook for 18 minutes more, until the noodles are tender.
Uncover and sprinkle the mozzarella over the top of the lasagna. Cover again and cook until the cheese is melted, about 5 minutes. Remove the pot from the heat.
Sprinkle the lasagna with parsley and serve with garlic bread alongside.