In a medium saucepan, cover quail eggs with cold water. Bring to a boil and simmer for 4 minutes. Drain water and immediately transfer eggs to a bowl with cold water and 1 cup ice cubes to chill.
While the quail eggs boil and chill, assemble the marinade. In a 1.5L jar (I use a large jam jar), add remaining ingredients: soy sauce, water, sugar, garlic, green onions, red pepper. Stir with spoon until sugar dissolves. Set aside.
When the quail eggs are cold, peel carefully. Immediately drop them into the marinade-filled jar. Repeat for all 18 eggs. Cover and refrigerate overnight.
When ready to serve, spoon eggs and sauce into a small serving dish for communal eating. Serve alongside other banchan. Or, if eating solo, spoon eggs and sauce directly on top of rice. Enjoy!