Heat a large nonstick skillet over medium-high heat and add the vegetable oil. Add the frozen hash browns, 3/4 teaspoon salt and a few grinds of pepper. Flatten the potatoes, cover and cook, without stirring, until starting to brown on the bottom, 3 to 5 minutes. Stir a few times, cover and cook, stirring occasionally, until mostly browned, about 15 minutes. (Reduce the heat to medium if the potatoes are browning too quickly.) Use a wooden spoon or spatula to shape the potatoes into 4 rounds.
Top the potato rounds with 2 roast beef slices each; season lightly with salt and pepper. Cover with 2 cheese slices each, then top with the red onion. Cover and cook over medium heat until the cheese is just melted, about 2 minutes; sprinkle with the chives.