Preheat oven to 350°F.
Quarter each biscuit and remove from the can; set aside.
Melt the butter in a large saucepan over medium-low to medium-high heat. Carrot, diced onion, and celery should be sauteed until the onion begins to mellow. Add the garlic and continue cooking for one minute.
Cook while incorporating the flour for one minute. Add the cooked chicken, broth, and bouillon, followed by the thyme. Cook until it comes to a simmer, then for one to two minutes. After removing from heat, incorporate the quarter biscuits. Transfer to a 9-by-13-inch baking dish.
Bake the biscuits for 15 minutes, or until golden and fragrant. Allow to sit for five minutes. As this dish cools, it will become thicker.