Add all tofu filling ingredients to a food processor or blender and pulse to combine, scraping down sides as needed. You are looking for a semi-pureed mixture with bits of basil still intact. Taste and adjust seasonings as needed.
Peel sweet potatoes and slice thinly with a very sharp knife or mandolin. They shouldn't be paper thin, but semi-thick and bendable - about 1/8th inch.
In a 9x13-inch (or similar size) dish, begin laying down the sweet potatoes in a single layer, overlapping slightly.
Top with one-third of the tofu ricotta mixture and spread using a spoon or spatula. Top with another layer of sweet potatoes, slightly overlapping. Repeat until you have three total layers of tofu ricotta, and four layers of sweet potatoes. The top layer should be sweet potatoes.
Cover with foil and bake for 50 minutes.
Then remove foil, increase oven heat to 400 degrees F (204 C), and bake uncovered for another 5-10 minutes to slightly brown up the top layer.
While the lasagna is cooking, prepare pesto (optional), by adding olive oil, basil, and garlic to a blender or food processor. Mix on on medium-low speed to combine. Then add vegan parmesan cheese, a pinch each salt and pepper and pulse to combine again.
Add water to thin until a pourable pesto sauce is achieved, mixing on high until only small bits of basil and garlic remain. Taste and adjust seasonings as needed. I added a bit more vegan parmesan cheese and basil.
Let lasagna cool slightly before serving. Top entire lasagna with desired amount of pesto, or reserve for individual servings.
Best when fresh, though leftovers keep covered in the refrigerator up to 3 days. Freeze for longer-term storage.
Taste and adjust seasonings as needed, adding more salt and pepper for flavor, nutritional yeast for cheesiness, and lemon juice for brightness.
*Nutrition information is a rough estimate calculated with half of the basil pesto sauce.