Soak the ribs in cold water for about 1 hour, changing the water several times.
Place ribs in a large pot and submerge in water until just covered. Bring to a boil and let simmer for about 30 minutes.
Drain.
Repeat step 2: in the same pot, submerge the ribs in water until just covered. Bring to a boil and simmer again for about 30 minutes. This time, let everything cool - about 6 hours - or until the layer of waxy fat forms at the top. Refrigerate once the pot is cooled.
In the meantime, prepare the marinade by mixing together the soy sauce, sesame oil, brown sugar, garlic cloves, black pepper, and pine nuts in a bowl.
Once the contents of the pot as completely cooled, you will see a layer of solidified fat at the top. Remove and discard as much of it as possible. Drain and save the remaining liquid.
Pour the marinade over the ribs and add enough reserved liquid to just cover the ribs. You don't want to completely submerge the ribs.
Bring to a boil. Lower heat and let simmer for about 3 hours or until the beef is fork tender. Add chestnuts during the last 30 minutes of cooking time.
While the ribs are cooking, the egg garnish can be prepared. Heat a couple of teaspoons of vegetable oil in a non-stick frying pan over medium heat. Add the egg and tilt the pan to form a thin layer of egg. Cook for about 2-3 minutes or until the top is firm. If the egg is thicker, you may want to flip it and cook for a few second. Let cool. What I like to do is to is to fold the egg over a couple of times and thinly slice the eggs, almost a chiffonade. (The Korean-style egg garnish is typically prepared by cooking the egg white and yolk separately so that you have white and yellow strips.)
Once the ribs are done, garnish with green onions and egg slices and serve family-style.