Combine the potatoes and onions in a salad spinner. Spin as much liquid as possible from the mixture, 1 to 2 minutes.
In a large mixing bowl, combine the potato mixture with the oil and divide into four equal parts.
Heat oven to 200 ̊F.
On the stove: Melt 1/2 tablespoon of the butter in a 10-inch skillet set over medium heat.
In a small mixing bowl, season one quarter of the potato mixture with salt and pepper and spread into a thin layer in the pan. Using a spatula, form the potatoes into a round, and press down gently. Brown for 5 to 7 minutes. Top the roesti with another 1/2 tablespoon of butter and slide onto a pan lid. Carefully invert the pan over the lid and flip the pan and lid back over (the raw side of the roesti should now be face-down in the pan). Return the pan to the heat and brown the roesti for an additional 5 to 7 minutes.
Remove to a wire rack and hold in a warm oven. Repeat previous steps for remaining potato mixture.
In a waffle iron: Heat waffle iron to its highest setting.
In a microwave-safe bowl, melt the butter on high for approximately 1 minute. Brush both sides of the hot waffle iron with about 1/2 tablespoon each of the melted butter.
Add one quarter of the potato mixture to the iron and spread into an even layer. Close the iron and cook for 8 to 10 minutes. Remove the roesti to a wire rack and hold in the warm oven. Repeat with the remaining 3 portions.