Step 1

Bring a large pot of salted water to a boil. Reduce heat, carefully add tofu, and simmer gently until slightly puffed and firmed up, about 4 minutes. Using a slotted spoon, transfer tofu to a medium bowl.

Step 2

Heat vegetable oil in a large heavy pot over medium-high heat. Add kimchi and gochujang and cook, stirring often, until beginning to brown, 5–8 minutes. Add kimchi liquid and 8 cups water. Bring to a boil, reduce heat, and simmer until kimchi is softened and translucent, 35–40 minutes.

Step 3

Add scallions, soy sauce, and tofu; simmer gently until tofu has absorbed flavors, 20–25 minutes (tofu will fall apart a little). Add sesame oil; season with salt and pepper. Ladle stew into bowls; top each with an egg yolk and sesame seeds.