Peel the potatoes and grate finely. Rinse in a colander, press out excess water and put in a bowl. Peel and grate the onions. Mix with the potatoes. Salt and pepper to taste.
Melt the butter and oil in the pan. Spoon the potatoes into the pan in a single layer or separate into four smaller patties. Cover and bake at high heat.
When the potatoes have begun to brown on the bottom, turn and brown on the other side. Cooking time will depend on the thick-ness of the potato patties, but around 30 minutes total.