Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9x13 inch baking dish.
In a skillet, melt the butter over medium-high heat. Cook and stir the garlic, onion, celery, and carrots in butter until tender. Mix in the flour, sugar, salt, 1 teaspoon dried basil, and pepper. Stir in broth, and bring to a boil. Stirring constantly, boil 1 minute, reduce heat, and stir in peas. Simmer 5 minutes, then mix in chicken. Transfer mixture to the prepared baking dish.
In a medium bowl, combine the baking mix and 2 teaspoons dried basil. Stir in milk to form a dough. Divide the dough into 6 to 8 balls. On floured wax paper, use the palm of your hand to flatten each ball of dough into a circular shape; place on top of chicken mixture.
Bake in the preheated oven for 30 minutes. Cover with foil, and bake for 10 more minutes. To serve, spoon chicken mixture over biscuits.