Preheat the oven:
Preheat your oven to 400°F (200°C). Lightly grease a 9×13-inch baking dish or casserole dish with cooking spray or butter.

Cook the vegetables:
In a large skillet, melt the butter over medium heat. Add the chopped onion, garlic, carrots, and celery. Cook for 5-6 minutes, stirring occasionally, until the vegetables are soft and fragrant.

Make the creamy filling:
Sprinkle the flour over the cooked vegetables and stir to coat evenly. Cook for 1-2 minutes to eliminate the raw flour taste. Slowly pour in the chicken broth while whisking to prevent lumps. Stir in the milk and cook for 3-4 minutes, or until the mixture thickens slightly.

Add the chicken and peas:
Stir the shredded chicken, frozen peas, thyme, parsley, salt, and pepper into the creamy mixture. Mix well, then transfer the filling to the prepared baking dish and spread it out evenly.

Prepare the biscuit topping:
In a medium bowl, combine the baking mix, milk, and cheddar cheese (if using). Mix until just combined. The dough will be slightly thick and spoonable.

Add the biscuit topping:
Drop spoonfuls of the biscuit dough evenly over the chicken mixture in the baking dish. It’s okay if some gaps remain between the biscuits.

Bake:
Place the casserole in the preheated oven and bake for 25-30 minutes, or until the biscuits are golden brown and the filling is bubbling around the edges. Let it cool for 5-10 minutes before serving.