If your chicken is not pre-cooked, prepare it now by cooking, then shredding or dicing into bite-sized pieces.

In a large pot or Dutch oven, melt 4 tablespoons of butter over medium heat. Add the chopped onion, celery, and carrots, cooking for 5-7 minutes until the vegetables soften.

Stir in 1/2 cup of all-purpose flour and cook for 1-2 minutes, stirring constantly, to create a thick paste known as a roux.

Gradually whisk in the chicken broth, followed by the milk or cream, continuing to whisk until the mixture thickens and comes to a simmer, which takes about 5-7 minutes.

Stir in the cooked chicken, frozen peas, frozen corn, fresh thyme, and fresh parsley. Season with 1 teaspoon of salt and 1/2 teaspoon of black pepper, then taste and adjust seasonings as needed.

Pour the creamy chicken filling into a 9x13 inch baking dish or a 3-quart oven-safe dish.

In a medium bowl, whisk together 2 cups of flour, baking powder, baking soda, and salt. Cut in the cold, cubed butter using a pastry blender, two knives, or your fingertips until the mixture resembles coarse crumbs with pea-sized pieces of butter.

Gently mix in the buttermilk until just combined, being careful not to overmix the dough.

Drop dollops of the biscuit dough evenly over the hot chicken filling. If desired, brush the tops of the biscuits with an egg wash or melted butter for extra browning.

Bake in a preheated oven at 375°F (190°C) for 25-30 minutes, or until the biscuit topping is golden brown and the filling is bubbly.

Remove from the oven and let rest for 5-10 minutes before serving, allowing the filling to set slightly.