Preheat the oven to 350°F (175°C) and grease a 9x13-inch baking dish.
Melt butter in a large skillet over medium-high heat. Stir in chopped onion, celery, carrots, and garlic. Cook until softened, about 5 minutes.
Whisk in the flour, sugar, salt, basil, and pepper to form a roux. Slowly add chicken broth, stirring constantly until the mixture comes to a boil. Let it boil for 1 minute until thickened. Reduce the heat, stir in peas, and simmer for 5 minutes.
Mix the cooked chicken into the skillet and stir until everything is well combined. Transfer this mixture into the prepared baking dish.
In a mixing bowl, combine the baking mix and dried basil. Stir in the milk until it forms a dough. Divide this dough into 6-8 balls and flatten each into a circular shape.
Arrange the biscuits on top of the chicken filling. Bake uncovered for 30 minutes, then cover with foil and bake for an additional 10 minutes.
Serve hot and spoon the creamy chicken mixture over each biscuit.
