Step 1

Combine kombu and 4 cups water in a large pot. Let sit until kombu softens, 25–30 minutes. Bring to a simmer over medium heat. Immediately remove from heat once water starts simmering; fish out kombu and discard. Add bonito flakes and stir once to submerge them. Return to a gentle boil, reduce heat, and simmer about 5 minutes. Remove from heat and let steep 15 minutes (this ensures you get the most flavorful broth, or dashi, possible).

Step 2

Meanwhile, cook eggs in a medium pot of boiling water 6 minutes. Transfer to a bowl of ice water (ice bath) and let sit until cold, about 2 minutes. Peel eggs; set aside.

Step 3

Strain dashi through a fine-mesh sieve into a medium bowl. Discard solids, wipe out pot, and return dashi to pot. Add kimchi and tofu and bring to a very gentle simmer. Remove from heat. Submerge sieve in liquid, add miso and gochujang to sieve, and stir to liquefy both, then press through strainer until pastes are dissolved.

Step 4

Divide soup among bowls. Top with sesame seeds and drizzle with sesame oil. Cut eggs in half and add to bowls.