For the pork: Preheat the oven to 300 degrees F.
Heat a large Dutch oven over medium-high heat, add the bacon and cook until the bacon is crisp and the fat is rendered, stirring occasionally, about 10 minutes. Remove the bacon with a slotted spoon and transfer to a plate.
Add the pork, skin-side down, to the same pot and sear until crisp and golden, about 4 minutes. Flip and cook an additional 5 minutes. Remove and transfer to the bacon plate.
Add the garlic, carrots, celery and onions to the same pot and cook until softened, about 5 minutes. Add the sake and simmer for 2 minutes. Add the pork and bacon back into the pot, and then add the soy sauce, 1 cup of water, the gochujang and sesame oil. Bring to a simmer, cover and transfer to the oven. Cook until the pork is falling off the bone, about 4 hours, basting the pork every hour. After 2 hours, add an additional cup of water.
Remove the pork to a board and let stand for about 10 minutes. While the pork is resting, use a ladle to skim off most, but not all, of the fat from the braising liquid. Set aside 1 cup of the chunky braising liquid and then add the brown sugar to the remaining braising liquid in the pot. Shred the pork with two forks and then add the meat back into the pot, mixing with the remaining braising liquid. Set aside the pork bone.
For the soup stock: Heat the canola oil in a large stockpot over high heat. Add the mushrooms, carrots, celery, garlic and onions and cook until soft, about 5 minutes. Add the reserved pork bone and chunky braising liquid, and cover with the chicken stock and 3 quarts of water. Bring to a boil, reduce to a simmer and cook for 2 hours. Strain the broth and add soy sauce to taste.
For the ramen and toppings: Cook the ramen noodles according to the package directions. Drain and set aside.
Prepare a medium bowl with ice water. Bring a small pot of water to a boil and add the eggs. Cook the eggs for 6 minutes, and then use a slotted spoon to transfer them to the ice water. While running the eggs under cold water, gently peel each one, being careful not to break the yolks. Place the eggs in a bowl and set aside.
To serve, divide the ramen between the bowls and ladle the broth over them. Add a heaping spoonful each of the shredded pork, corn and kimchi to each of the bowls. Place an egg in each bowl and sprinkle the scallions on top. Fold a sheet of nori in quarters and tuck on the side of each bowl.