Make the Tomato Sauce - In a large saucepan, heat olive oil over medium-low heat. Sauté the onions and garlic for about 3 minutes. Add the tomato paste and stir. Add the crushed tomatoes and oregano. Simmer over low heat for 30 minutes, and cover with the lid slightly open. Season with salt and pepper to taste.
Heat the Oven - Preheat the oven to 350°F (177ºC). Lightly grease a 13 by 9-inch baking dish with olive oil or cooking spray.
Cook the Lasagna Noodles - In a large pot, cook noodles in salted boiling water according to the package directions. Cook a few extra noodles in case they break. Drain with a colander and lay them on a clean towel to dry and cool.
Cook the Vegetables - In a large saute pan, heat olive oil over medium-high heat. Add the spinach, kale, and zucchini and saute until wilted, about 3 minutes. Cool slightly.
Make the Filling - In a large bowl, combine the vegetable mixture with ricotta, parmesan, ⅔ cup mozzarella, salt, pepper, and nutmeg (if using).
Assemble the Lasagna Rolls - Spread 3 to 4 tablespoons of filling over the length of each noodle (8 total). Leave about ½-inch of space at the end so the cheese does not come out as you roll. Roll the noodles from bottom to top, but not too tight.
Bake - Place the rolls in the greased baking dish side by side. Pour about 1 cup of tomato sauce evenly on top. Sprinkle the remaining ⅓ cup mozzarella. Bake for 20 to 25 minutes until heated through and the sauce is bubbling.
To Serve - Combine the diced tomato and basil together in a small bowl. Serve lasagna rolls topped with the mixture and fresh chopped parsley.
Notes
Make Ahead: The unbaked lasagna rolls can be assembled, covered, and refrigerated up to 2 days in advance. Freeze the rolls for up to 1 month. It can be baked from frozen, just add more time as needed.
Storing: Cover and refrigerate leftovers for up to 3 days, or freeze for 1 month.