Preheat your oven to 400°F (200°C). Lightly grease a 9x13-inch baking dish or deep skillet.
In a large skillet or saucepan, melt butter over medium heat. Add diced onion and sauté for 3–4 minutes until softened. Stir in garlic and cook for 30 seconds.
Add flour and cook for 1 minute, stirring constantly. Slowly whisk in chicken broth and milk until smooth. Let it simmer until thickened, about 3–5 minutes.
Stir in chicken, peas and carrots, thyme (if using), and season with salt and pepper to taste. Transfer the filling to the prepared baking dish.
In a large bowl, whisk together flour, baking powder, garlic powder, and salt. Cut in the cold butter with a pastry cutter or fork until mixture resembles coarse crumbs. Stir in shredded cheese and milk until just combined (do not overmix).
Drop spoonfuls of the biscuit dough evenly over the top of the chicken filling.
Bake for 25–30 minutes, or until the biscuits are golden brown and cooked through.
Mix melted butter, garlic powder, and chopped parsley. Brush over the tops of the hot biscuits right after baking.
Let cool slightly before serving. Scoop and enjoy each bite of creamy filling with cheesy biscuit topping.