Cook lasagna noodles in a 2-quart saucepan according to package directions. Drain and toss with a teaspoon of oil. Set aside.
Using the same saucepan, saute onions in oil over medium-heat for 2 minutes.
Add the minced garlic and cook for an additional 30 seconds, stirring frequently.
Add the ground beef to the pot, breaking it up as it cooks. Stir in red pepper flakes, oregano, and salt. Cook until the beef is brown, approximately 3 minutes.
Stir in tomato paste, tomato sauce, and broth. Bring the soup to a simmer.
Add the heavy cream and bring the soup to a brief boil, stirring occasionally.
Return the cooked lasagna noodles to the pot. Stir in Parmesan and mozzarella cheeses until they melt into the soup.
Pour the soup into a bowl and garnish with basil leaves before serving.