Heat the butter in a large wide pot over medium heat until melted. Add the carrot, celery and garlic and cook, stirring occasionally, until the vegetables are soft, about 5 minutes. Add the broth and bring to a boil.
Stir in the gnocchi and cook until al dente, 3 to 5 minutes. Stir in the frozen peas and chicken and cook until warmed through, about 3 minutes. Remove from the heat, stir in the dill and season with salt and pepper.
Divide the soup among 4 bowls, sprinkle with Parmesan and serve with crusty bread on the side.
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