Use scissors to thinly slice the scallions, then use them to snip the kimchi into small pieces. In a medium saucepan, heat the kimchi, gochujang, oil and half the scallions over medium-high. Stir until the colors are muted, 1 to 2 minutes.
Add 2 ½ cups water, the soy sauce and gochugaru. Once boiling, taste the broth for salt (add soy sauce) and heat (add gochugaru, or if it’s too spicy, add a pinch of sugar). Add the noodles and cook until just tender according to package directions.
Crack the egg, if using, into the pot. Reduce heat to medium-low, cover and steam until the whites are cooked but the yolk is still soft, 2 to 3 minutes.
Scoop the tofu into a bowl, then spoon the soup over top. Garnish with the reserved scallions.
