In a large pot, melt the butter over medium heat. As it melts, let the rich aroma fill the air, setting the stage for what’s to come.
Add the chopped onion, diced carrot, and diced celery. Cook, stirring occasionally, until the vegetables are softened, about 5 to 7 minutes. You want them to be tender and fragrant, creating a delightful base.
Next, add the minced garlic and cook for an additional 1 minute until fragrant. The garlic will start to release its wonderful aroma, enhancing the flavor of your soup.
Stir in the flour to coat the vegetables, cooking and stirring constantly for about 2 minutes. This step helps to create a roux, which will thicken the soup beautifully.
Slowly pour in the chicken broth while stirring continuously to prevent lumps. Alternatively, you can whisk the broth well with a whisk to ensure there are no flour lumps. Watch the soup come together as it thickens slightly.
Add the dried thyme and bay leaf to the pot. These herbs will infuse the soup with wonderful flavors as it simmers.
Bring the soup to a gentle boil, then reduce the heat and let it simmer for about 10 minutes, covered, stirring occasionally. This allows all the flavors to meld together beautifully.
Stir in the shredded cooked chicken and milk. This is where the soup gets its creaminess and heartiness. Let it simmer for another 5 minutes until heated through and slightly thickened.
Finally, remove the bay leaf and season with salt and pepper to taste. Taste it to ensure the flavors are just right, then serve warm. Enjoy!