Arrange the potatoes in a 9-by-13-inch baking dish and season with the dried oregano and a good pinch of salt. Drizzle with the oil and toss to coat with your fingers. Roast for about 1 hour. (I went 1 hour and 10 minutes, just for extra browning.)
Remove the potatoes from the oven and switch the oven to broil.
Sprinkle the grated cheese over the potatoes and arrange the pepperoni in a single layer over the cheese. Broil for 2 to 3 minutes; don't take your eyes off it (see Cook's Note)! This happens fast, and all we want is browning and bubbling, and for the pepperonis to crisp and curl. Serve immediately with pizza sauce and a sprinkle of parsley or chives!
When I broiled the dish, I put it right back on the baking rack, not the very tiptop rack normally used for broiling. So if you put it on the top rack, it may take right under 2 minutes.