Preheat the oven to 375 degrees F.
Cook the noodles to al dente according to the directions on the package. Drain them well and spread them out onto aluminum foil or waxed paper to prevent them from sticking.
Heat the oil in a large saute pan over medium-high heat. Add the mushrooms and cook, stirring occasionally, until browned and all the liquid has evaporated, about 5 minutes. Season with 1/4 teaspoon of the salt. Stir in 1 1/2 cups of the tomato sauce and simmer for 2 minutes. In a medium bowl, combine the ricotta cheese, spinach, egg, the remaining 1/4 teaspoon salt, a few turns of pepper and nutmeg.
Spread 1 cup of the tomato sauce on the bottom of a 9- by 12-inch baking dish. Spread about 2 tablespoons of the ricotta mixture onto a lasagna noodle. Top with about 1 1/2 tablespoons of the mushroom mixture, roll the noodle and place it into the baking dish. Repeat with the remaining noodles. Spread the remaining 1 1/2 cups sauce over the lasagna rolls. Top with the grated cheeses, cover loosely with foil and bake for 45 minutes. Uncover and bake for 15 minutes more.
In a large pot, heat the oil over medium heat. Add the onions and cook, stirring occasionally, until soft, about 5 minutes. Add the garlic and cook for 2 minutes longer. Add the tomato paste, dried oregano, whole tomatoes and bay leaf, and cook, uncovered, stirring occasionally, until thickened, about 30 minutes. Season with salt and pepper.
From Food Network Kitchens; after further testing and to ensure the best results this recipe has been altered from what was in the actual episode.