Heat the oven to 200°F. Set a wire rack on a sheet pan, or line a large plate with paper towels, so you have a place to hold the cooked fritters warm.

Put the grated potatoes in a colander in the sink. Sprinkle the salt over them and toss with your hands, then let them stand for 5 minutes so they release some water.

While the potatoes stand, chop the kimchi and save 1 tablespoon of brine from the jar. Slice the scallions, keeping the whites and greens separate.

Put the grated cucumber in a clean kitchen towel or a thick layer of paper towels. Squeeze firmly over the sink until the cucumber feels much drier.

Stir the squeezed cucumber, Greek yogurt, reserved kimchi brine, and half of the scallion greens together in a small bowl. Set the bowl aside for serving.

Gather the potatoes in the towel and squeeze hard over the sink until as much liquid as possible has come out. Transfer the dry potatoes to a large mixing bowl.

Add the chopped kimchi, scallion whites, the remaining scallion greens, the beaten eggs, the flour, and the black pepper to the bowl with the potatoes. Stir until the flour disappears and the mixture holds together when you press a spoonful against the side of the bowl.

Pour 2 tablespoons of the oil into a large nonstick skillet and set it over medium-high heat. When the oil looks shiny and moves easily across the pan, tilt the skillet to coat the bottom.

Scoop heaping 1/4-cup mounds of the potato mixture into the skillet, cooking 4 fritters at a time. Flatten each mound with the back of a spoon into a round about 1/2 inch thick.

Cook the fritters on the first side for 3 to 4 minutes. They are ready to turn when the edges look set and the bottoms are deep golden brown.

Flip the fritters with a thin spatula. Cook the second side for 3 to 4 minutes, until it is browned and the center feels firm when lightly pressed.

Transfer the cooked fritters to the rack or paper towel-lined plate, then move them to the warm oven. Add another 2 tablespoons of oil to the skillet.