Set a large pot over medium heat and add the olive oil. When the oil is hot, add onion, celery, and carrots. Cook for 5 minutes, stirring occasionally, until the vegetables are softened and fragrant. Add garlic and continue cooking for an additional 30 seconds.

Add the chicken-style broth and half-and-half to the pot with the sautéed vegetables. Stir well and heat gently, but do not boil.

Reduce the heat to low and add the gnocchi, Italian seasoning, poultry seasoning, and ground black pepper. Simmer for 8–10 minutes, stirring occasionally, until the gnocchi are tender and the soup has thickened slightly. If you prefer a thicker soup, simmer a little longer to reduce.

Adjust seasoning to taste. Ladle the soup into serving bowls and garnish with fresh parsley and a generous sprinkle of Parmesan cheese. Serve hot.