Preheat oven to 350 F.
Bring a large pot of water to a boil over medium high heat. Add tortellini and cook according to package directions, about 8-10 minutes. Drain with a colander, and set aside. Meanwhile, heat oil in a large cast-iron skillet (or oven safe skillet) for 2 minutes over medium-high heat until the hot oil sizzles and shimmers. Add sausage and cook for 5-7 minutes until browned. Break the sausages into small pieces using a spatula. Add onions and sauté until tender, about 3-4 minutes. Stir well to combine.
Add in tomato sauce, parsley, salt and pepper. Stir well to mix and bring to a simmer. Turn the heat down to low, and simmer uncovered for 5 minutes.
Add in the cooked tortellini and stir well to fully coat it in sauce. Sprinkle shredded mozzarella and grated Parmesan evenly on top of the tortellini.
Transfer the skillet into the oven and bake for 10-12 minutes, until the cheese melts and turns golden brown. Remove from oven, and let cool for 5 minutes before serving.
Garnish with extra parsley and Parmesan cheese on top.