Warm a soup pot or Dutch oven over medium-high heat and melt the butter. Introduce the chopped onion, celery, and carrot slices, allowing them to sauté for 5 to 7 minutes with occasional stirring until they become tender and faintly golden.
Incorporate the sliced mushrooms and minced garlic into the pot and continue sautéing for another 5 minutes, stirring intermittently until the vegetables have softened.
Sprinkle in the flour and stir without pause for approximately 1 minute, ensuring it takes on a golden hue.
Gradually pour in the chicken stock, followed by the sliced potatoes, salt, and black pepper. Elevate to a boil, then lower the heat to maintain a simmer. Partially cover and allow to cook for 12 to 15 minutes, or until the potatoes are just tender.
Stir in the shredded chicken, frozen peas, and corn along with the heavy cream and chopped parsley. Let the soup return to a gentle simmer and continue cooking for an additional 5 minutes, or until the vegetables are tender throughout. Adjust seasoning with more salt and pepper to taste and remove from heat.