Prepare the jangahjji. Scrub the cucumbers until clean. Slice cucumbers, jalapeno, and radish into ¼ inch thick slices. Place into a glass jar.
Heat sugar, soy sauce, vinegar and salt in a medium saucepan over medium heat. Cook until the sugar has dissolved, stirring occasionally. Bring to a simmer. Remove from heat and pour soy sauce mixture in the jar onto the cucumber mix. Let cool to room temperature. Cover the jar and let sit overnight.
To make the soup, soak the beef short ribs in cold water in a large bowl. Let sit for 20 minutes.
Drain ribs and rinse. Place in a large pot and cover with cold water. Cover and bring to a boil over high heat. Uncover and let boil rapidly for 10 minutes to remove any impurities. Remove from heat, drain and rinse the ribs. Thoroughly wash the pot.
Place ribs back into the pot and fill with 12 cups water. Add whole onion, garlic, and ginger into the pot. Cover and bring to a boil. Reduce heat to low and continue to simmer for 1 hour 30 minutes or until the ribs are tender. The meat should easily fall apart from the bone.
Strain the broth, discarding the onion, garlic, and ginger. Set aside the short ribs. Bring the strained broth back to a boil. Add the radish and cook until tender, about 15 minutes. Return the short ribs to the broth and season the soup with salt and pepper.
Meanwhile, cook the noodles according to the directions on the package.
Heat 1 teaspoon oil in a nonstick saute pan over medium-low heat. Add the whisked eggs and spread in an even layer to create an egg crepe. Cook for one minute. Flip and cook on the other side until the eggs have set. Remove from heat and slice into thin strips. Set aside.
Portion the glass noodles into 6 bowls. Ladle soup on top with short ribs and radish. Garnish with egg strips and chopped green onions. Serve with rice on the side and jangahjji.