Heat the oven to 400°F and bring a large pot of water in a boil.
Heat a tablespoon of the olive oil in a medium frying pan over medium-high heat.
Add the sausage and cook it until it loses its pink color, breaking it into smaller pieces with a slotted spoon, about 10 minutes. Using the spoon, transfer the sausage in a large bowl and set it aside.
Wipe the frying pan clean with a paper towel.
Heat the remaining 2 tablespoons of oil in the saucepan over medium-high heat. Add the onion and cook it until it is soft, about 3 minutes.
Add the garlic and cook it until fragrant, about 1 minute.
Pour in the broth and cook for 1 minute more.
Stir in the tomatoes, basil, ½ teaspoon of the salt, and ¼ teaspoon of the pepper and cook for another 10 minutes. Taste the sauce and adjust the seasoning if necessary.
Mix the ricotta, mozzarella, peas, Parmesan, egg, the remaining ½ teaspoon salt and 1/4 teaspoon pepper, and the nutmeg with the bowl of cooked sausage. Stir to combine well, then set the mixture aside.
Add the tablespoon of salt to the boiling water, then drop in the lasagna pasta. Boil it for one minute, stirring every few seconds in keep it from sticking.
Drain the pasta and rinse it under cold running water until it's cool enough to handle. Separate the pasta sheets and lay them out on a clean, dry kitchen towel.
Cover the bottom of a 9 x 13-inch pan with one cup of the sauce.
Spread a dollop of the filling (about 1/3 cup) across a short end of a pasta sheet and roll it up. Put the roll in the prepared pan. Repeat the process with the remaining filling and pasta. (You should have enough to fill 12 rolls.)
Top the cannelloni with the rest of the sauce and bake them until heated through, about one hour (plus). Serve hot, with Parmesan for sprinkling.
January 18, 2014 Carlos and I made this for a dinner together with Bea, Patty and Kathlene. Carlos did a great job! It was well received. Doubled recipe to send second pan home with P. and K. Needed about three more jars of sauce, even after doubling recipe, but needed less than one box of lasagna noodles for the whole doubled batch. Made 27 rolls. Yummy. Topped with extra mozzarella for last half hour of baking.