Step 1

Preheat oven to 200°. Grate sweet potatoes on the large holes of box grater or in a food processor with the grater disk. Transfer to a clean kitchen towel or several layers of paper towels. Gather ends of towel and squeeze over a large bowl to wring out as much liquid as possible; discard liquid. Wipe out bowl and place sweet potatoes, eggs, kimchi, flour, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt in bowl; season with pepper. Mix batter with a fork to combine.

Step 2

Pour oil into a large cast-iron or nonstick skillet to come ¼" up sides; heat over medium-high until shimmering. Drop heaping tablespoonfuls of batter into skillet, taking care not to crowd. Using a heatproof spatula, gently flatten fritters. Cook until undersides are browned and crisp, about 2 minutes. Turn over and cook until browned and crisp on the other side, about 2 minutes. Transfer fritters to a rimmed baking sheet lined with several layers of paper towels and let drain. Transfer to a wire rack set inside a rimmed baking sheet and slide into oven to keep warm. Repeat with more oil and remaining batter.

Step 3

Mix yogurt and gochujang in a small bowl; season with salt. Transfer fritters to a platter and serve with gochujang yogurt for dipping.