Use a wide heavy pot with a lid, about 4 quarts in capacity. Heat olive oil over medium heat and soften onion for 5 minutes. Add garlic and tomato paste; cook 1 minute, stirring until the paste darkens slightly without burning.

Add crushed tomatoes, broth, salt and pepper and bring to a gentle boil. Stir in the dry pasta and make sure it is mostly submerged. Reduce to a steady simmer and leave the lid slightly ajar.

Cook 12–16 minutes, stirring every 1–2 minutes and scraping the bottom to prevent sticking. Start tasting at the packet's minimum cooking time; the acidic sauce can make it take longer. Add hot water in 1/4-cup increments if liquid runs low before the pasta is tender.

When the pasta is just tender and a little loose sauce remains, reduce heat to low. Stir in cream and Parmesan and warm 1–2 minutes without a hard boil. If the sauce is already thick, add another splash of water before the cheese.

Remove from the heat and fold in basil. Rest 2 minutes, then divide among four bowls. The sauce thickens as it stands; loosen leftovers with water rather than extra cream. Taste before adding more salt because the broth and Parmesan vary in saltiness.