01 - Preheat oven to 400°F. Lightly grease a 9x13-inch baking dish and set aside.
02 - In a large skillet over medium heat, melt 2 tablespoons butter. Add diced onion and cook until translucent, about 3 minutes. Stir in minced garlic and cook for 1 additional minute.
03 - Sprinkle 3 tablespoons flour over the onion and garlic. Cook, stirring constantly, for 1 minute to form a roux.
04 - Slowly whisk in chicken broth, then whole milk. Continue stirring and cooking until the mixture thickens, about 2 to 3 minutes.
05 - Add shredded chicken, thawed peas and carrots, corn, dried thyme, sea salt, and black pepper. Stir to combine and simmer on low for 3 minutes. Pour the filling into the prepared baking dish.
06 - In a large bowl, whisk together flour, baking powder, garlic powder, sugar, and salt. Cut in cold cubed butter using a pastry blender or fork until the mixture resembles coarse crumbs.
07 - Stir in shredded cheddar cheese and chopped parsley. Pour in milk and mix just until combined, being careful not to overmix.
08 - Drop spoonfuls of the biscuit dough evenly over the chicken filling to cover the surface.
09 - Bake for 25 to 30 minutes until the biscuit topping is golden brown and cooked through.
10 - While baking, combine melted butter, garlic powder, and chopped parsley in a small bowl.
11 - Remove cobbler from the oven and immediately brush the tops of the biscuits generously with the garlic herb butter. Let cool for 5 minutes before serving.