Preheat the oven to 375°F (190°C) and lightly grease a 9x13-inch baking dish.
Bring a large pot of salted water to a boil. Add the diced potatoes and cook for 8 to 10 minutes until just barely fork-tender. Drain well.
Melt the butter in a large skillet over medium heat. Add the onion and cook for 4 to 5 minutes until softened.
Stir in the garlic and cook for 30 seconds until fragrant.
Sprinkle the flour over the onion mixture and cook for 1 minute, stirring constantly.
Gradually whisk in the milk and chicken broth until smooth. Stir in the garlic powder, onion powder, thyme, salt, and black pepper, then simmer for 3 to 5 minutes until slightly thickened.
Remove the skillet from the heat and stir in 1½ cups of the cheddar cheese and the Parmesan until melted and smooth.
Gently fold the cooked chicken and potatoes into the cheese sauce until evenly coated.
Transfer the mixture to the prepared baking dish and sprinkle with the remaining cheddar cheese.
Bake for 25 to 30 minutes, or until the casserole is hot and bubbly. Broil for 2 to 3 minutes if desired for a golden cheese topping. Let the casserole rest for 10 minutes before garnishing with fresh parsley and serving.