Wash potato well and prick several time with a fork. Place on a microwave safe plate and microwave for 5 to 6 minutes. Half way through cooking process, flip them over. Peel potato and cut into 1-inch pieces.
Heat a large skillet over medium high heat, add cooking oil, leek, garlic and generous pinch of salt and pepper. Cook them until leek is soften, about 3 minutes.
Add ground beef and season with generous pinch of salt and pepper. Breaking up meat with wooden spoon until brown, about 5 minutes.
Stir in kimchi, gochugaru and soy sauce. Sauté everything together until kimchi is soften, about 5 minutes.
Stir in butter and potato. Using back of wooden spoon or spatula, gently pack into skillet and cook, without stirring for 1 to 2 minutes. Flip hash with a spatula, 1 portion at a time, and lightly repack into skillet. Add additional butter if needed. Repeat flipping process every couple minutes until potatoes are browned, about 5 to 7 minutes.
Reduce heat to low or turn of the heat for a moment, then make 4 shallow wells in hash. Crack 1 egg into each well and season with salt and pepper. Cover and cook over medium low heat until white are set and yolks are runny, about 3 to 5 minutes. Sprinkle with chive and serve while it’s hot! Enjoy!