Preheat oven to 450°F and line a baking sheet with parchment paper or foil.
Put potatoes in a large pot and add water to cover. Bring to a boil then reduce heat and simmer for 25 minutes or until potatoes are tender when pierced with a fork. Potatoes should be cooked through but still hold their shape. Do not overcook. Drain potatoes and let cool for 10 minutes.
Place potatoes on baking sheet and gently press down on each with the palm of your hand until they split open but are still in one piece and are about 1/2-inch thick. Space potatoes 1-inch apart. Brush with oil and flip to coat both sides.
Sprinkle potatoes with salt and pepper and cook for 20 minutes. Sprinkle Parmesan, lemon zest and rosemary over potatoes and toss lightly; cook for 10 to 15 minutes more or until potato edges are crispy and brown.
Serve warm with Greek yogurt sprinkled with green onion tops.