In a large pot, melt the butter over medium heat. Add the diced onion, carrots, and celery, cooking until the vegetables are softened, about 5-7 minutes.
Stir in the minced garlic and diced mushrooms, cooking for an additional 2-3 minutes until fragrant and mushrooms have softened.
Sprinkle the flour over the vegetables and stir well to combine, cooking for 1-2 minutes to eliminate the raw flour taste.
Gradually whisk in the cold whole milk or half and half, making sure to incorporate it smoothly with the flour mixture.
Slowly add 3 to 4 cups of low sodium chicken broth while stirring, creating a creamy base. Adjust broth amount based on preferred soup thickness.
Add the salt-free seasoning blend and stir to combine.
Mix in the cooked, shredded chicken, frozen peas, and frozen corn. Simmer the soup for about 10 minutes, allowing flavors to meld and vegetables to heat through.
Stir in the shredded white cheddar and cook until melted and fully incorporated.
Season the soup with salt and pepper to taste.
Finally, add the cooked egg noodles to the soup, stirring gently to combine. Serve hot.