Preheat the oven to 350 degrees. Lightly grease a 9×13 inch casserole dish. In a large deep skillet, melt the butter over medium-high heat. Add garlic, onion, celery and carrots and stir-fry in the butter until tender. Mix in flour, sugar, salt, 1 teaspoon of dried basil, and pepper. Stir in chicken broth and bring to a boil. Boil for 1 minute while stirring constantly. Reduce heat and stir in peas and simmer for 5 minutes. Mix in the chopped cooked chicken. Transfer the mixture into the prepared baking dish.
Arrange refrigerated biscuits in a single layer over the chicken mixture in the casserole dish.
Place into the oven and cook for 30 minutes at 350 degrees until the mixture is bubbling and the biscuits are browned on top and fully cooked.