Put the pork ribs into a medium pot and cover them with room temperature water. Bring the water to a rolling boil over high heat, then lower the heat to medium and briskly simmer the ribs for 5 minutes. Drain the pork in a colander in the sink, then rinse it under cool, running water to remove any scum.
Heat a wok over high heat and swirl in the canola oil. Add the ginger and the pork ribs and cook, stirring often, until the pork is slightly browned and the edges of the ginger have curled, about 4 minutes. Pour 6 cups of water into the wok, then add the scallion. Bring the mixture to a rolling boil and cook until the broth gets cloudy, about 10 minutes.
Transfer the pork, ginger and broth to a clean pot set over low heat. Cover the pot with a tight-fitting lid and gently simmer the soup until the ribs are soft and tender, 1–1½ hours.
When the pork is tender, add the winter melon to the pot. Continue to simmer everything until the melon is translucent and tender, but not mushy, about 20 minutes. Season the broth with the salt, adding more if you’d like. Remove and discard the ginger and scallions.
Drizzle some toasted sesame oil into the soup, adjusting to taste. Divide it into soup bowls and enjoy while hot.
