In a large Dutch oven or soup pot, melt 6 tablespoons of butter over medium-high heat. Add the chopped onion, celery, and sliced carrots. Sauté for 5-7 minutes, stirring occasionally, until the vegetables are softened and lightly golden.
Add the sliced mushrooms and minced garlic to the pot. Continue sautéing for another 5 minutes, until the mushrooms have softened and released their moisture.
Sprinkle the flour over the vegetables and stir constantly for 1 minute, allowing the flour to cook until it turns golden.
Pour in the chicken stock and add the sliced potatoes, 3 1/2 teaspoons salt (or to taste), and black pepper. Bring the mixture to a boil, then reduce the heat to a simmer. Partially cover and cook for 12-15 minutes, or until the potatoes are tender.
Add the shredded chicken, frozen peas, frozen corn, heavy whipping cream, and chopped parsley. Stir well and bring the soup back to a simmer. Cook for an additional 5 minutes, until the peas and corn are tender.
Taste the soup and adjust the seasoning with more salt and pepper if needed. Remove from heat and serve hot, garnished with extra parsley if desired.