Heat oil in a 6-quart pot over medium heat and cook onion for 5 minutes. Add garlic and tomato paste for 1 minute, then peppers, broth, basil, salt and pepper.
Simmer for 8 minutes until onion is very soft. Blend the broth smooth with an immersion blender, keeping the blade submerged.
Add turkey and return to a gentle simmer for 5 to 7 minutes until pieces reach 165°F.
Add gnocchi and cook according to the package, about 3 to 5 minutes, until tender. Fold in spinach until wilted.
Stir in cream and warm gently for 1 minute without boiling hard. Serve promptly while the dumplings remain distinct.