01 - Preheat oven to 400°F. Lightly grease a 9x13-inch baking dish with butter or nonstick spray and set aside.
02 - In a large skillet over medium heat, melt 2 tablespoons of butter. Add the diced onion and cook until softened and translucent, about 3 minutes. Stir in the minced garlic and cook for 1 additional minute until fragrant.
03 - Sprinkle 3 tablespoons of flour over the onion and garlic mixture. Stir continuously and cook for 1 minute to remove the raw flour taste and form a smooth roux.
04 - Slowly whisk in the chicken broth, followed by the whole milk. Continue stirring and cooking over medium heat until the sauce thickens and coats the back of a spoon, about 2 to 3 minutes.
05 - Add the shredded chicken, thawed peas and carrots, corn, dried thyme, sea salt, and black pepper to the sauce. Stir everything together until well combined and simmer gently on low heat for 3 minutes. Pour the filling evenly into the prepared baking dish.
06 - In a large mixing bowl, whisk together the flour, baking powder, garlic powder, sugar, and salt until evenly distributed.
07 - Add the cold cubed butter to the flour mixture. Using a pastry blender or fork, cut the butter into the dry ingredients until the mixture resembles coarse crumbs with some pea-sized pieces remaining.
08 - Fold in the shredded cheddar cheese and chopped parsley. Pour in the milk and stir gently just until the dough comes together. Be careful not to overmix, as this will make the biscuits tough.
09 - Drop generous spoonfuls of the biscuit dough evenly across the surface of the chicken filling, spreading slightly to cover as much area as possible.
10 - Place in the preheated oven and bake for 25 to 30 minutes, or until the biscuit topping is golden brown and cooked through and the filling is bubbly.
11 - While the cobbler bakes, combine the melted butter, garlic powder, and chopped parsley in a small bowl and mix well.
12 - Remove the cobbler from the oven and immediately brush the tops of the hot biscuits generously with the garlic butter mixture. Allow the cobbler to rest for 5 minutes before serving.