3 lb. (1.5 kg) boneless pork shoulder, cut into 3 equal pieces
Kosher salt, to taste
2 Tbs. canola oil
1 yellow onion, coarsely chopped
6 garlic cloves, chopped
2-inch (5-cm) piece fresh ginger, peeled and chopped
8 cups (64 fl. oz./2 l) low-sodium chicken broth
1 leek, white and green parts, halved lengthwise and coarsely chopped
4 oz. (125 g) cremini or button mushrooms, brushed clean and coarsely chopped
Low-sodium soy sauce for seasoning
Sesame or chile oil for seasoning
1 1⁄2 lb. (750 g) fresh ramen noodles
4 green onions, white and pale green parts, finely chopped
Season the pork with salt.
Put a large sauté pan or the stove top–safe insert of a slow cooker on the stove top over medium-high heat, then add the oil and warm until hot. Working in batches if necessary to avoid crowding, add the pork pieces and sear them on the first side without moving them until well browned, 3 to 4 minutes. Turn the pieces and sear on the second side until well browned, 3 to 4 minutes longer. Transfer to a plate and set aside.
Pour off all but 2 Tbs. of the fat from the insert or sauté pan and return the insert to medium-high heat. Add the yellow onion and sear, without stirring, until browned, about 5 minutes. Stir in the garlic, ginger, and 1 cup (8 fl. oz./250 ml) of the broth and deglaze the sauté pan or insert, stirring and scraping up any browned bits from the insert bottom, then let simmer for 1 minute.
If using a sauté pan, transfer the contents of the pan to the insert of a slow cooker. Add the leek, mushrooms and the remaining 7 cups (56 fl. oz./1.75 l) broth and stir to combine. Cover and cook on the low setting for 8 hours. The pork should be very tender and the broth should be fragrant.
Transfer the pork to a cutting board. Using 2 forks, break the pork into bite-size chunks, removing and discarding any large pieces of fat. Strain the broth through a fine-mesh sieve into a bowl and discard the solids. Using a large spoon, skim off and discard any fat from the surface of the broth. Return the pork and broth to the slow cooker and season to taste with soy sauce and sesame or chile oil. Cover and cook on the low heat setting for about 30 minutes to warm through.
Cook the ramen noodles according to the package directions. Put the eggs into boiling water and simmer for 5 to 6 minutes. Remove the eggs from the water, let cool until they can be handled and peel them. Cut each in half lengthwise.
To serve, divide the noodles evenly among individual bowls. Ladle the broth and pork over the noodles, dividing them evenly, then sprinkle with the green onions. Top each bowl with two soft-boiled egg halves and serve immediately. Serves 8.