Heat the olive oil in a 10-inch nonstick, oven-safe skillet over medium-high heat until it begins to shimmer. Add the onion and cook, stirring, for 3 to 4 minutes, or until they begin to brown. Add the potato and water. Lower the heat to medium, cover the pan, and let the potato cook for 8 to 10 minutes, checking occasionally, until the potato is tender and the water has evaporated. If there’s some residual water, uncover the pan and let it boil off. If the water boils off before the potato is tender, add a splash more.
Once the potato is soft, add the sauerkraut, salt, and pepper and stir to combine. Evenly spread out the ingredients in the pan and add the eggs. Using a silicone spatula, work the beaten eggs into the vegetable mixture and give the pan a gentle wiggle to help it settle.
Transfer the pan to the oven and bake for 8 to 10 minutes, or until the top puffs and turns light brown. Switch your oven to the BROIL setting and broil for 1 to 2 minutes, to brown the top of the frittata.
Remove the pan from the oven and let the frittata cool for a minute or two. Slide a silicone spatula around the edges of the pan to loosen the eggs. Transfer the frittata onto a large cutting board and slice into wedges.