How to Make It
Whisk together butter and oil in a small bowl. Reserve 2 teaspoons of butter mixture for later. Heat remaining butter mixture on 1 side of a large nonstick skillet over medium-high. Place hash browns on buttered side of skillet in a round shape about 5 inches wide. Cook, undisturbed, about 5 minutes, until browned and crisp around edges.
Flip hash browns, and cook, undisturbed 4 to 5 more minutes, until other side is browned and crispy. Meanwhile, add reserved butter mixture to other side of skillet; add onion. Cook, stirring often for 2 minutes. Add ham to onion, and cook 2 minutes. Add onions and ham to top of cooked hash browns. Top with cheese slice; turn off heat. Let stand until cheese is melted; serve immediately.