Fried Potatoes with Oregano and Parmesan

¼ cup EVOO
1 ½ lb Yukon Gold potatoes (about 5); peeled and halved lengthwise, then cut crosswise into ¼ inch thick slices
1 lg onion, halved lengthwise, then sliced lengthwise
¾ tsp dried oregano, crumbled
½ tsp salt
¼ tsp black pepper
3 tbsp finely grated parmigiano-reggiano

Heat oil in a 12 inch nonstick skillet over moderately high heat until hot but not smoking, then add potatoes, onion, oregano, salt, and pepper and reduce heat to moderate. Cook, covered, stirring and turning potatoes over occasionally, until almost tender, about 10 minutes. Remove lid and cook, stirring and turning potatoes over 3 or 4 times, until browned and crusty, 8 to 10 minutes more. Add salt and pepper to taste, then transfer to a shallow bowl and sprinkle with cheese.