Add the potatoes, onion, cheese, garlic powder, rosemary, salt, and black pepper to a large bowl and mix until thoroughly combined.

Heat olive oil and butter in a large cast iron skillet over medium heat until the butter is melted. Carefully swirl the skillet to ensure the bottom is evenly covered.

Working in batches, add the potatoes to the skillet and shape into patties. Cook until golden brown, approximately 4-5 minutes before flipping. Cook for another 4-5 minutes, or until golden brown and crispy.

Remove hash browns from skillet and keep warm. Repeat Step #3 with remaining potato mixture. Add more olive oil to the skillet, as needed.

Remove from heat and transfer hash browns to individual serving plates. Serve immediately with your choice of sides. Enjoy!