Brown the beef. Heat 1 tbsp olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add 500g (1 lb) ground beef and cook for 6–8 minutes, breaking it into small crumbles, until deeply browned with crispy edges. Do not stir constantly — let the meat sit undisturbed for 2–3 minutes at a time so it sears rather than steams.
Build the flavor base. Reduce heat to medium. Add 1 diced medium yellow onion and cook 4–5 minutes until softened and translucent. Add 4 minced garlic cloves and cook 30 seconds until fragrant. Push the mixture to the sides, add 2 tbsp tomato paste to the cleared center, and cook 1–2 minutes, stirring, until it darkens to a brick-red color. Stir everything together, then add 1 tsp Italian seasoning, 1 tsp oregano, ½ tsp paprika, ½ tsp salt, ¼ tsp black pepper, and ½ tsp sugar.
Add tomatoes and broth. Pour in 1 can (400g / 14 oz) crushed tomatoes, 1 can (400g / 14 oz) diced tomatoes with their liquid, and 900ml (4 cups) beef broth. Stir, scraping the bottom of the pot to release the browned bits. Bring to a boil, then reduce to a steady simmer.
Cook the noodles. Once boiling, add 8–10 broken lasagna noodles (roughly 5cm / 2-inch pieces, about 200g / 7 oz dry). Stir to separate. Simmer uncovered for 10–12 minutes, stirring occasionally, until the noodles are al dente. Taste and adjust salt — add more if needed. If the soup thickens too much, stir in up to 240ml (1 cup) extra broth or water.
Serve with the cheese topping. While the noodles cook, mix 250g (1 cup) ricotta with a pinch of salt and black pepper in a small bowl. Ladle the hot soup into bowls. Top each with a generous dollop of the seasoned ricotta, a handful of shredded mozzarella (150g / 1½ cups total), a sprinkle of parmesan (30g / ⅓ cup total), and torn fresh basil (2 tbsp). Serve immediately.