Peel and chop the potatoes into large pieces. Drop them over into a large pot filled with cold water and about 1 tsp of salt. Bring the pot to a boil and cook until the potatoes are soft and easily pierced with a knife. (large pieces) and boil potatoes; mash or grate coarsely (you want some texture). Allow to cool.
Thoroughly drain the cooked potatoes, then coarsely mash them with a fork or potato masher (see note for variation). Set them aside to cool somewhat.
Finely dice the onion. Add the onion, flour, eggs, salt, and pepper to the mashed potatoes. Mix well.
Preheat oven to 300°F (150°C).
Heat about 1.5 tbsps of butter and 1 tbsp of oil in a a large skillet over medium heat on the stove top.
Wet your hands thoroughly, then form the mixture into small balls (about the size of a large egg). Don't worry if they're particularly sticky. Drop the balls into the pan - and fry in butter until golden brown and easy to flip - about 3 minutes per side. Don't overcrowd the pan.
Transfer the fried cakes to a baking sheet. Repeat with remaining batter, adding a little more butter and oil whenever the pan begins to get a bit dry.
Place the baking tray in the oven and bake for about 15-20 minutes (but see note on potato varieties), or until the cakes are well-set but still creamy inside. If you cook a full batch, I recommend frying enough to fill a single tray, then placing these in the oven while you fry more cakes for a second tray.
Serve the finished cakes warm, with prepared sides.