In a large stock pot or dutch oven over medium-high heat, melt butter.
Add carrots, celery, mushrooms, and shallots. Stir to coat in the melted butter. Cook for a couple of minutes, constantly stirring.
Add salt & pepper, and continue cooking until carrots are tender, about 8-10 minutes. Turn the heat down slightly if necessary.
Add garlic, poultry seasoning, and thyme, and stir until garlic is nice and fragrant, about 1-2 minutes.
Add flour by sprinkling into the pot evenly, and stir until every bit is coated in flour, and cook for another minute.
Add chicken stock and milk, and stir until blended.
Bring to a bubbling boil and add gnocchi. Reduce heat to medium so it is lightly bubbling. Cook until gnocchi is done, about 5 more minutes.
Add shredded chicken and peas. Taste, and add more salt & pepper if needed.
To serve, divide the gnocchi dish among 4 bowls. Serve with a crusty bread for dipping.