Heat the neutral oil and sesame oil in a pot over medium heat. Add the onion and cook 2 minutes until it softens.
Add the gochugaru and garlic and stir constantly for 30 to 45 seconds. The flakes should bloom in the oil and turn it brick red. Do not let them darken past that or the stew tastes burnt.
Pour in the stock, soy sauce, and fish sauce. Add the mushrooms or zucchini if using. Bring to a boil.
Spoon the sundubu into the pot in big rough scoops. Do not stir it smooth; the soft curds are the point. Simmer 4 minutes.
Drop in the prawns and simmer 2 to 3 minutes, just until they curl and turn pink. They keep cooking in the hot broth, so pull the pot off the heat the moment they look barely done.
Crack the eggs straight into the bubbling stew, one per serving. Cover for 1 minute for set whites and runny yolks, or stir them through for an egg drop texture.
Top with scallions and serve with rice.