Preheat oven to 450ºF. Set a 10" cast iron pan inside the oven for at least 10 minutes.
In a small bowl, whisk the eggs and milk together.
In a larger bowl, whisk the flour, sea salt, and Gochugaru. Slowly pour in the egg and milk mixture, whisking until incorporated.
Remove the pan from the oven, and add the butter. Swirl the pan to coat it with the melting butter, making sure to coat the entire bottom and sides of the pan.
Pour batter in the pan, and sprinkle the diced green onion evenly across the batter.
Bake at 450ºF for approximately 20 minutes, or until the pancake is large and golden. Turn the oven temperature to 250ºF, slightly open the oven door, and bake 5 more minutes.
While the Dutch baby bakes, whisk together the Korean dipping sauce ingredients. Set aside.
Drain the olive oil from the sardines into another pan. Heat the oil over medium heat until it ripples.
Add an egg to the pan, and cook it sunny side up. Discard the peppercorns from the sardine tin, and add the fish to the hot pan.
When the egg is cooked, and the sardines are hot, remove them from the pan. Cover to keep warm.
Pour the dipping sauce into the hot pan, and simmer 1 minute. Pour into a serving dish.
Serve the Dutch baby with the egg, sliced avocado, and sardines. Top with the green onion garnish, and serve with the dipping sauce.