1. In a large stockpot filled with salted boiling water, add the potatoes and cook until tender when pierced with a knife, 20 to 25 minutes.

2. Meanwhile, in a medium skillet set over medium heat, melt 3 tablespoons of the butter and add the onion. Cook until the onion is softened but not colored, about 5 minutes.

3. Remove the potatoes from the water and, once cool enough to handle, carefully peel off and discard the skins. In a large bowl and while the potatoes are still hot, use a fork to mash the potatoes until they are semi-smooth. Add the cooked onions to the potatoes. Stir in the caraway seeds and parsley and season with salt and pepper. Add the flour and mix until well combined. Use your hands to knead the potatoes until smooth, then roll the potatoes out to a ¾-inch-thick round (about 8 inches in diameter) and use the top of a drinking glass or a 2½-inch-round cutter to cut into circles.

4. In a medium skillet set over medium-high heat, add the remaining tablespoon of butter. When the butter is melted, add the potato cakes and fry, flipping once until golden on each side, 3 to 4 minutes per side. Serve hot.