Step 1: Preheat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
Step 2: Par-cook the diced potatoes. Place potatoes in a large pot, cover with cold water, and bring to a boil. Cook for 5-7 minutes, or until tender-crisp but not fully soft. Drain well.
Step 3: In a large saucepan or Dutch oven, melt the butter over medium heat. Whisk in the flour and cook for 1-2 minutes, stirring constantly, until a light roux forms.
Step 4: Gradually whisk in the milk until smooth. Bring the mixture to a gentle simmer, stirring frequently, until the sauce begins to thicken.
Step 5: Reduce heat to low. Stir in the garlic powder, onion powder, salt, and pepper. Add 1 1/2 cups of the shredded cheddar cheese and all of the Monterey Jack cheese, stirring until melted and smooth.
Step 6: In the prepared baking dish, combine the par-cooked potatoes, diced chicken, and broccoli florets.
Step 7: Pour the creamy cheese sauce over the potato mixture and stir gently to ensure everything is evenly coated.
Step 8: Sprinkle the remaining 1/2 cup of shredded sharp cheddar cheese over the top of the casserole.
Step 9: Bake for 25-30 minutes, or until the casserole is hot, bubbly, and the cheese on top is golden brown. Let rest for 5-10 minutes before serving. Enjoy!