Step 1Bring 1 gallon water to boil in large pot. Add brisket. Reduce heat and simmer 2 to 3 hours or until liquid reduces to 2/3.
Step 2Soak rice cakes in cold water 1 hour.
Step 3Scramble yolks and whites of eggs separately. Fry yolks into a thin omelet in small nonstick skillet over high heat, 1 minute per side. Fold or roll up omelet and slice into thin strips. Repeat with egg whites. Set aside.
Step 4Remove brisket from pot and reserve for another use. Increase heat for stock to high. Bring to boil and add soup stock. Add rice cakes. Reduce heat to medium and cook until ovalettes have softened, about 10 minutes.
Step 5Serve hot in large bowls garnished with sliced egg whites, egg yolks, Bulgogi, green onions and seaweed. Season with salt and pepper to taste.