Place the potatoes into a large pot and cover with salted water; bring to a boil. Cook the potatoes at a boil for 10 minutes; drain. Set potatoes aside to cool.
Once potatoes are cool enough to handle, slide the skin from the potatoes and discard; refrigerate peeled potatoes until completely cold, about 1 hour.
Preheat an oven to 350 degrees F (175 degrees C).
Grease a 9×13-inch baking dish with 1 tablespoon butter.
Grate 2 of the potatoes into the bottom of the prepared baking dish. Sprinkle about 1/4 of the minced onion and Dubliner cheese over the layer of potato; season with salt and white pepper. Repeat layering until all ingredients are used and dish is full.
Drizzle melted butter, greek yogurt, and milk over the potato mixture; season with paprika.
Bake in the preheated oven until the top is bubbling, about 30 minutes.
Garnish with chopped fresh green onions and parsley to serve.