Preheat the oven to 375ºF. Grease a 9×13-inch casserole dish.
Melt the butter in a saucepan over medium heat. Add the onion and cook until softened. Stir in the flour, then whisk in the milk and cream until smooth and thickened.
Stir in 1 cup cheddar, garlic powder, paprika, salt, and black pepper.
Spread the hashbrowns in the prepared dish. Pour the sauce over and toss gently to coat.
Top with the remaining cheddar, Parmesan, and breadcrumbs.
Bake uncovered for 30–35 minutes, until bubbly and golden. Let rest for 5–10 minutes, then garnish with chives.
6 servings