To make the chicken and dumplings, start by heating the oil in a large pot over medium heat. Add the celery, carrots, and onion, and cook for about 5 minutes until the vegetables are soft. Stir in the garlic, flour, thyme, salt, and pepper, and cook for another minute.

Bring the mixture to a boil before adding the chicken broth. At a low heat, simmer for about ten minutes. Stir in the shredded chicken and cook for another 5 minutes.

In a separate bowl, whisk together the biscuit mix and milk until smooth. Drop the dough by tablespoonfuls into the pot with the chicken mixture. The dumplings should be cooked through in about ten minutes. Stir in the melted butter and serve hot.

Note: This recipe makes about 6 servings. You can adjust the quantities of the ingredients to suit your taste and the size of your pot. Enjoy!