Julienne the cucumber and take the egg out of the fridge to warm it up.
Boil water and add the noodles.
Once softened, mix it around to loosen up and cook evenly. Cook until al dente.
Take out the noodles using a tong or chopsticks, then place them on a plate. Keep the noodle water in the pot.
Add the oil to the noodles and mix to keep them from sticking.
Leave ½ cup of noodle water in the pot and discard the rest, then add the vegetable and seasoning packet.
Place the pot on medium-high heat, mix the sauce around using the handle of the pot, and cook until thickened up–you should notice that the sauce kind of coats the bottom of the pot. This will take about 5 minutes.
Lightly oil a pan and place it on medium heat. Add the egg, cover, and cook it for 2 minutes–the whites should be cooked while the yolk should be runny.
Pour the sauce over the noodles, top with the egg, and garnish with gochugaru and cucumber.
Serve with kimchi, and enjoy!