Heat the olive oil in a large pot over medium heat. Cook the pancetta until crisp, about 5 minutes. Add the onion, carrots, and celery and cook until softened, 6 to 7 minutes, then stir in the garlic for 30 seconds.

Sprinkle in the flour and stir for 1 minute. Gradually whisk in the broth and cream, add nutmeg, salt, and pepper, and simmer for 5 minutes.

Add the gnocchi and simmer until they float and the broth thickens, about 3 to 4 minutes.

Remove from heat and stir in the spinach until wilted. Ladle into bowls, top with Parmesan, and serve hot.