Combine potatoes and onions in a tea towel. Squeeze as much liquid as possible from the mixture. In a large mixing bowl, combine this mixture with the oil and divide into four equal parts.
In a 10-inch non-stick saute pan melt 1/2 a tablespoon of butter. Season one part of potato mixture with salt and pepper and spread into a thin layer in the pan. Brown for 5 to 7 minutes. Invert the roesti onto pan lid and remove pan from heat. Add additional 1/2 tablespoon of butter to the preheated pan. Slide roesti into pan raw side down and brown for an additional 5 to 7 minutes. Remove to a rack and hold in a warm oven. Repeat previous steps for remaining potato mixture.