Heat a Dutch oven or large soup pot over medium-high heat and melt the butter.
Add the chopped onion, celery, and sliced carrots, then sauté for 5 to 7 minutes, stirring occasionally, until softened and lightly golden.
Add the sliced mushrooms and minced garlic, then sauté for another 5 minutes, stirring occasionally, until softened.
Sprinkle in the flour and stir constantly for 1 minute, until the flour turns lightly golden and coats the vegetables.
Gradually pour in the chicken stock while stirring to help prevent lumps.
Add the sliced potatoes, salt, and black pepper, then bring the soup to a boil.
Reduce the heat to a simmer, partially cover the pot, and cook for 12 to 15 minutes, or until the potatoes are tender but still hold their shape.
Stir in the shredded chicken, frozen peas, frozen corn, heavy whipping cream, and chopped parsley.
Bring the soup back to a gentle simmer and cook for 5 minutes, or until the chicken is heated through and the peas and corn are tender.
Taste and adjust the salt and black pepper as needed, then remove the pot from the heat and serve warm.