In a large pot, melt 1 tablespoon of butter over medium-high heat. Add the onion, carrot, and celery, sautéing for 3 minutes. Then, add the garlic and continue to sauté for an additional minute.

Next, pour in the chicken broth, then add the potatoes, thyme, rosemary, and bay leaves. Season with salt and pepper to taste.

Cover the pot and bring the soup to a gentle boil, then reduce the heat to medium-low. Press the vegetables down into the broth and let it simmer, stirring occasionally, until the potatoes are nearly tender, about 15 minutes.

In the meantime, in a medium saucepan over medium heat, melt the remaining 5 tablespoons of butter. Stir in the flour and cook the mixture for 1 ½ minutes, stirring constantly. While whisking, gradually pour the milk into the flour mixture.

Season the mixture with salt and pepper to taste. Continue cooking, stirring constantly, until it thickens (avoiding boiling). Then, stir in the cream and remove from heat, covering with a lid.

Once the potatoes are nearly tender, add the peas and corn to the soup with the vegetables, and heat through for a few minutes.

Stir the milk mixture and chicken into the soup. If you prefer a thinner consistency, you can add a bit of chicken broth as needed.

Remove the bay leaves, then stir in the parsley. Serve the soup warm, enjoy.