Cook the onion.
Pat the chicken dry and season lightly with salt and black pepper. Heat the sun-dried tomato oil in a large pot or Dutch oven over medium-high heat. Add the chicken in a single layer and cook for about 4 to 5 minutes, turning until browned on several sides. The chicken does not need to be completely cooked at this stage. Transfer it to a plate.
Reduce the heat to medium and add the butter. Add the onion and cook for 3 to 4 minutes until softened. Scrape any browned chicken bits from the bottom of the pot as the onion releases moisture.
Add the garlic, chopped sun-dried tomatoes, tomato paste, Italian seasoning and red pepper flakes. Cook for about 1 minute, stirring constantly. The tomato paste should darken slightly without sticking or burning.
Add the broth.
Pour in the chicken broth and scrape the bottom of the pot again. Return the browned chicken and any juices from the plate. Bring the broth to a gentle simmer and cook for about 5 minutes.
Cook the gnocchi in the soup. Add the gnocchi directly to the pot. Simmer according to the package timing, usually 3 to 5 minutes. Most potato gnocchi rise toward the surface once they are nearly cooked.
Add the cream. Lower the heat and stir in the heavy cream. Keep the soup below a hard boil once the cream goes in.
Finish with Parmesan and spinach.
Turn off the heat. Add the Parmesan a little at a time, stirring until it melts into the broth. Fold in the spinach and let the residual heat wilt it for 1 to 2 minutes.
Check the seasoning. Taste before adding more salt. Parmesan, broth and sun-dried tomatoes already contribute plenty of salt. Add black pepper, extra chili flakes or basil before serving.
