Cover the almonds with boiling water and soak for 10-15 minutes. Rinse and drain and add to a high-powered blender along with the remaining vegan ricotta ingredients.
Start blending on low speed and gradually increase the speed to medium-high. Blend until no chunks of almonds remain and the consistency is creamy and resembles traditional ricotta. Stop to scrape down the sides as needed and stir the mixture around with a silicone spatula to re-incorporate any chunks of nuts. Add more water if needed and blend again. Be careful not to blend too high or overblend, as the consistency will become paste-like.
Preheat oven to 375°F.
Warm ½ cup vegetable broth in a 12-inch non-stick skillet over medium-high heat. Add the carrots and sauté for 5 minutes, stirring frequently.
Add the other ½ cup vegetable broth along with the broccoli and eggplant. Season with salt to taste. Sauté for 3 more minutes, stirring frequently.
Add the spinach a little at a time, stirring constantly until wilted enough to add more until all spinach has been used and is wilted (approximately 3 minutes). Remove from the heat and set aside until ready to use.
Line the bottom of a 9" x 13" baking dish with 1 ½ cups tomato sauce. Add the first layer of lasagna sheets (4 sheets) in the sauce-lined baking dish.
Use half of the ricotta mixture and dollop an equal amount onto each lasagna sheet. Spread around evenly using a small silicone spatula or spoon. Evenly distribute half of the veggie mixture over the ricotta layer. Pour 1 cup of sauce over top of the veggie layer. Add another layer of lasagna sheets and press each one down lightly. Repeat this process 1 more time, using the other half of the ricotta and the other half of the veggie mixture.
Pour the remaining sauce over top of the lasagna, and use a spatula or spoon to spread the sauce around, ensuring all parts of the lasagna sheets are covered by sauce so that they do not dry out.
Cover with aluminum foil and bake for 35 minutes. Remove foil and bake for 10 more minutes.
After removing from the oven, top with vegan Parmesan and fresh chopped basil, if desired. Allow to cool for 10-15 minutes before cutting into pieces and serving.