Combine the flour and salt in a stainless steel bowl. Whisk together the egg, sour cream and water and stir into the flour. Lightly knead together into a ball. Wrap in plastic wrap and refrigerate for an hour. Meanwhile, make the filling. Peel the potatoes and cut into large dice.
Place in a large saucepan and cover with water. Season with salt and simmer for 15 minutes until the potatoes are tender. Drain in a colander and allow the potato to dry slightly. Mash potatoes with the sour cream until smooth. Stir in the kimichi and green onions. Taste and season with salt.
To assemble the pierogies, remove the dough from the refrigerator and roll on a lightly floured work surface to a ¼-inch thick. Cut into 3½- inch circles with a pastry cutter. Gather all the scraps up and reroll the dough once more. Cut more circles and then discard any remaining dough. Place a spoonful of the potato filling in the center of each circle. Brush one side of the perimeter with a little water. Fold the dough over and pinch the edges together. Seal with the tines of a fork. Place on a sheet pan.
To make the sauce, combine the gouchjang, soy sauce, rice wine vinegar, brown sugar and ginger in a stainless steel bowl. Stir to combine and thin to light sauce consistency with a tablespoon of water or two if necessary.
Fill a wide-bottom pan with water and bring to a boil. Add 6-8 pierogis to the pan and cook until they float to the top. Remove from the pan and allow to drain on a towel. Repeat with the remaining pierogies. Heat a skillet over high heat with the enough oil or duck fat to come to a depth of one inch. Once the oil is hot slide a few of the pierogis into the oil without crowding the pan or dropping the temperature of the oil. Cook until golden brown. Turn over on to the other side and cook until brown and crisp. Remove to a paper towel-lined plate and repeat with the remaining pierogies. Lightly brush the pierogies with the gouchjang mixture and garnish with the chopped green onions and toasted sesame seeds.