Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9x13-inch baking dish.

Melt butter in a large skillet over medium-high heat. Cook and stir onion, celery, carrots, and garlic in hot butter until tender. Mix in flour, sugar, salt, basil, and pepper. Stir in broth; bring to a boil. Boil and stir for 1 minute, then reduce heat and stir in peas. Simmer for 5 minutes, then mix in cooked chicken until combined. Transfer to the prepared baking dish.

Make biscuits: Combine baking mix and basil in a large bowl. Stir in milk to form a dough. Divide dough into 6 to 8 balls. Use the palm of your hand to flatten each dough ball on floured wax paper into a circular shape; place on top of chicken mixture.

Bake in the preheated oven for 30 minutes. Cover with foil and continue baking for 10 more minutes. Spoon chicken mixture over biscuits to serve.