Slice the pork belly into thin, bite sized pieces. Cut the sour kimchi into bite sized pieces and set aside with ¼ cup (60 ml) of the brine. Slice the tofu into ½ inch (1 cm) thick pieces, thinly slice the onion, mince the garlic, and separate the green onion whites from the greens.
Set your pot over medium high heat and add 1 tablespoon toasted sesame oil. Add the sliced pork belly and cook, stirring, for 4 to 5 minutes until the fat starts to render and the edges brown.
Add the chopped kimchi, sliced onion, and green onion whites to the pot with the pork. Stir fry everything together for about 5 minutes, until the kimchi softens and takes on a slightly caramelized edge.
Push the pork and kimchi to one side and add the minced garlic, gochugaru, gochujang, and doenjang to the pot. Stir the pastes and spices in the oil for about 1 minute until fragrant, then mix everything together.
Pour in 2 cups (480 ml) anchovy stock and the ¼ cup (60 ml) kimchi brine you set aside. Stir in the soup soy sauce and sugar, then bring the pot to a boil. Reduce the heat to a steady simmer and cook uncovered for 15 minutes so the flavors meld and the broth reduces slightly.
Gently lay the sliced tofu into the simmering broth, nestling the pieces so they're mostly submerged. Simmer for another 5 minutes to heat the tofu through without breaking it apart. Taste the broth and adjust with a pinch more sugar if it's too sour, or a splash more soy sauce if it needs salt.
Scatter the green onion greens over the top and turn off the heat. Serve the stew piping hot straight from the pot with a bowl of steamed white rice on the side. Let it sit for a minute before diving in, since the broth stays scorching hot for a while.