In a large deep skillet over medium-high heat, melt the butter. Add the onion and cook for 2 to 3 minutes until softened.
Sprinkle the flour, salt, pepper, and garlic powder over the onions and stir to coat evenly. Pour in the chicken-style broth, reduce heat to low, and simmer for about 3 minutes, stirring frequently, until slightly thickened. Remove from heat.
Stir in the sour cream, 2 cups of cheddar, and ¼ cup of Parmesan until smooth and creamy.
Add the cubed potatoes to the skillet and stir to coat evenly with the cheese sauce.
Prepare a 6-quart slow cooker with non-stick cooking spray or a liner. Add the coated potatoes, cover, and cook on low for 4 hours until the potatoes are cooked through.
Add the remaining cheddar and Parmesan on top, replace the lid, and allow the cheese to melt for about 15 minutes.
Garnish with fresh chives and serve hot.