Melt butter in a Dutch oven over medium-high heat.
Sauté onion, celery, and carrots until softened and lightly golden, about 5–7 minutes.
Add mushrooms and garlic; cook until mushrooms release moisture and soften, about 5 minutes.
Sprinkle flour over vegetables; stir constantly for 1 minute.
Gradually whisk in chicken stock, then add potatoes, salt, and pepper.
Bring to a boil, reduce to simmer, cover partially, and cook until potatoes are tender, about 12–15 minutes.
Stir in chicken, peas, corn, cream, and parsley.
Simmer until peas and corn are heated through, about 5 minutes.
Adjust seasoning, remove from heat, and garnish with extra parsley.