Heat the olive oil: In a large pot or Dutch oven over medium-high heat, add the olive oil. Once the oil begins to shimmer, add the diced onion.

Cook the onion: Sauté the onion until softened and golden brown, about 5 minutes.

Add garlic: Stir in the minced garlic and cook until aromatic, about 1 minute.

Tomato paste: Add the tomato paste, stirring occasionally, and cook until it turns a brick-red color, about 2 minutes.

Cook the beef: Add the ground beef, salt, black pepper, red pepper flakes, oregano, and rosemary. Cook the beef, breaking it up with a wooden spoon, until browned and cooked through, about 5 minutes.

Add tomatoes: Crush the whole tomatoes by hand and add them to the pot along with the tomato juice from the can.

Add stock: Pour in the chicken stock and bring the soup to a low boil, stirring to combine.

Cook noodles: Add the broken lasagna noodles and cook until al dente, following the package instructions.

Prepare cheese mixture: While the noodles cook, combine the ricotta, Parmigiano-Reggiano, and mozzarella in a small bowl.

Serve: Ladle the lasagna soup into bowls and top each with a dollop of the ricotta mixture and fresh basil leaves.