Grate potatoes using a food processor or a box grater. Transfer the potatoes to a bowl.
Sprinkle salt over the potatoes and mix everything together with your hands or a spatula. Let the potatoes sit for about 10 minutes. This will help draw out moisture from the potatoes.
Place half of the potatoes into a towel. Wrap up the potatoes and wring out all the excess liquid (there will be a lot). Transfer the potatoes to another bowl.
Add the curry powder, garlic powder and black pepper to the potatoes and stir to incorporate.
Heat a 10-inch cast-iron skillet or non-stick pan over medium heat. Swirl in 2 teaspoons of olive oil. Once the pan is hot, add half of the potatoes. Spread out the potatoes into a 7 to 8 inch cake and flatten everything with the back of a spatula. Cook for about 3 to 4 minutes, or until the potatoes are golden brown. (This may take a few more minutes on your oven.) Using a rubber or silicone spatula, loosen the bottom of the rösti.
Turn off the heat. Cover the pan with a large plate (large enough to cover the pan completely). While holding on to the plate, flip the pan over so that the rösti lands on the plate.
Turn the heat back on to medium and swirl in another 1/2 tablespoon of oil. Slide rösti back into the pan and fry the other side for about 3 to 4 minutes. Transfer rösti to a serving plate.
Repeat steps 5 to 7 for the remaining potatoes. Serve röstis with fried eggs or vegetables!