Warm the olive oil in a large pot over medium heat.
Brown the sausage, breaking it up as it cooks; spoon off excess fat if needed.
Stir in onion, carrots, and celery; cook until softened, about 5 minutes.
Add garlic and tomato paste; cook, stirring, until fragrant and darkened slightly, 1 minute.
Pour in diced tomatoes and chicken broth; season with Italian seasoning, red pepper flakes, pepper, and salt.
Bring to a gentle boil, then simmer 10 minutes to meld flavors.
Add the ravioli and cook at a lively simmer until just tender, 5 to 7 minutes.
Reduce heat to low; stir in heavy cream and spinach. Cook until spinach wilts, 1 to 2 minutes. Adjust seasoning.
Ladle into bowls and top with Parmesan and basil.