Make the cashew ricotta and set aside.
Preheat oven to 400° 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.
Dollop ¼ cup of the ricotta mixture 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.
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 the 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.