Heat 1 tablespoon of olive oil in a large pot or Dutch oven over medium-high heat. Add 1 pound of Italian sausage and cook for 5 to 7 minutes, using a spoon to break it into small crumbles, until it is browned and no longer pink.
Add the finely chopped onion and cook for 3 to 4 minutes until it becomes soft and translucent. Stir in the minced garlic and cook for 1 more minute until it becomes fragrant.
Pour in 4 cups of chicken broth and the entire jar of marinara sauce, stirring to combine. Bring the soup to a boil over high heat.
Once boiling, add the broken lasagna noodles to the pot. Reduce the heat to a gentle simmer and cook for 10 to 12 minutes, stirring occasionally, until the noodles are tender and al dente.
Turn off the heat and stir in 1/2 cup of heavy cream, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. The soup will become creamy and slightly orange in color.
In a small bowl, combine the ricotta cheese and mozzarella cheese to make a dollop for serving.
Ladle the hot soup into bowls. Top each serving with a generous dollop of the cheese mixture and a sprinkle of fresh basil.