Preheat oven to 375°F and lightly grease a 9x13-inch baking dish.
In a large skillet over medium heat, melt the butter.
Add diced onion and celery. Sauté until softened, about 5 minutes.
Stir in salt, pepper, and flour. Cook for 1 minute to form a roux.
Gradually whisk in chicken broth and milk. Cook until thickened, about 5 minutes.
Stir in cooked chicken and thawed vegetables. Mix well and transfer to the baking dish.
Prepare the butter swim biscuit dough according to recipe instructions.
Spread the biscuit dough evenly over the top of the chicken mixture.
Bake uncovered for 35–40 minutes or until biscuits are golden brown and cooked through.
Let rest 10 minutes before serving.