Set your oven to 400°F and place a large ovenproof skillet on medium heat.
Add butter to the skillet and melt it, then whisk in 1/4 cup flour to form a roux, cooking for a minute or two.
Slowly pour in chicken broth and 3/4 cup milk, stirring constantly until the mixture thickens smoothly.
Mix in the cooked chicken, peas and carrots, thyme, salt, and pepper, and let everything simmer gently for a few minutes to blend flavors.
In a separate bowl, stir together 2 cups flour, baking powder, garlic powder, onion powder, cheddar cheese, and a pinch of salt.
Pour in 2/3 cup milk and the melted butter, mixing just until the biscuit dough comes together.
Spoon biscuit dough evenly over the hot chicken filling in the skillet, spacing them apart.
Transfer the skillet to the oven and bake uncovered for about 20 to 25 minutes, until the biscuits turn golden and are cooked through.
Once baked, sprinkle chopped fresh parsley over the top and allow the pot pie to cool slightly before serving.