Cut the potatoes into large chunks. (You can peel the potatoes if you don’t like the texture of the skins, or leave the peels on and remove some or all of the skins after peeling.) Place in a large saucepot and cover with water. Set over high heat and bring to a boil. Boil the potatoes for 10-15 minutes, until fork-tender.
Drain the potatoes. Peel off the skins (or some of the skins) if desired. Place the potatoes back in the pot. Use a potato masher to mash the potatoes. Based on your preference, you can roughly mash them, or mash them until smooth.
Then stir in the eggs, parmesan cheese, flour, scallions, and salt. Mix well.
Preheat the oven to 225 degrees F, to act as a warmer. Set a baking sheet in the oven. Set a large skillet over medium heat on the stovetop.
Add one tablespoon butter to the skillet. Use a 3 tablespoon scoop to portion out 6-8 potato cakes into the melted butter. Use the back of a spatula to smash them flat, about ½ - ¾ inch thick. Fry the potato cakes for 3-5 minutes per side.
Move the fried potato cakes to the warm oven. Repeat in small batches until all the potato mixture is gone.
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Notes
Once the cakes are cooled to room temperature, transfer to an airtight container and keep in the refrigerator for 4-5 days. Reheat in a skillet or warm for 10-15 minutes in a preheated 350 degree oven.They also freeze very well! I suggest you make the full Potato Cake recipe or even double the batch, and enjoy half now and freeze the rest for later. Wrap individual cakes in plastic wrap, and place all together in a sealed bag for up to 3 months in the freezer.