Set your oven to 400°F and warm up a large oven-safe skillet over medium heat.
Add butter to the skillet and melt it, then whisk in 1/4 cup flour to form a roux; cook this mixture for about 1 to 2 minutes.
Slowly pour in the chicken broth and 3/4 cup of milk while whisking constantly, stirring until the sauce thickens and becomes smooth.
Mix in the shredded chicken, frozen peas and carrots, dried thyme, salt, and pepper; allow the filling to simmer for 2 to 3 minutes and adjust seasoning as needed.
In a bowl, blend together 2 cups flour, baking powder, garlic powder, onion powder, shredded cheddar, and a pinch of salt.
Pour in 2/3 cup milk and melted butter to the dry ingredients and stir gently until just combined, forming the biscuit dough.
Spoon biscuit dough over the hot filling in the skillet, spacing the dollops apart.
Place the skillet in the oven and bake uncovered for 20 to 25 minutes, until the biscuits turn golden and are cooked through.
Once baked, sprinkle fresh parsley on top and let it sit a few minutes before serving to cool slightly.