Preheat oven to 350°F and set a pot of salted water to boil. Poke sweetpotatoes all over with a fork. Wrap each in a damp paper towel and microwave together on high, until fork-tender, 6 to 8 minutes total.
Meanwhile in a food processor, combine the basil, spinach, pine nuts, olive oil and garlic; blend until smooth.
When sweetpotatoes are cool enough to touch, remove the skin.
Add the ricotta, half of the mozzarella, the Parmesan cheese and peeled sweetpotatoes to the pesto in the food processor; whirl until smooth. Season to taste with salt and black pepper.
Line two large baking sheets with wax paper. Spread 3/4 cup of the tomato sauce onto the bottom of a 9- by- 13-inch baking pan.
When water comes to a boil, add the lasagna noodles. Cook until just al dente. Using a pair of tongs, remove the noodles from the cooking water and place them next to each other on the baking sheets.
Divide the sweetpotato filling onto the noodles and spread to cover them. Beginning at one end, loosely roll each noodle. Place the rolls, seam side down, into the baking pan with the tomato sauce, fitting them as snugly against each other as possible. Top with the remaining tomato sauce. Cover pan with aluminum foil; bake for 30 minutes.
Remove foil, add remaining mozzarella; bake, uncovered, until cheese starts to brown, about 15 minutes. Remove from oven and cool 5 minutes before serving.