Cook bacon in large nonstick skillet over medium-high heat until crisp, about 8-10 minutes. Using a slotted spoon, transfer bacon to large bowl (reserve drippings in skillet). Add potatoes to bacon, toss to combine. Sprinkle with salt and pepper.
Preheat broiler. Melt butter in same skillet with bacon drippings over medium heat. Form potato mixture into four 4-inch-diameter patties. Add potatoes to skillet. Cook until golden brown and cooked through, about 6 minutes per side. Transfer patties to baking sheet. Sprinkle cheese on top of patties. Broil patties until cheese melts, about 1 minute. Remove from broiler and serve.