Cook the ramen according to the package's instructions. Drain, rinse under cold water and drain again. Mix and blend well the ramen with the egg and the spice packet.
Oil the inside of 8 deep, flat-bottom salad bowls and divide the ramen mix. Press the noodles into the bottoms of the dishes with the bottom of a glass and refrigerate for about 30 minutes.
Heat 1 Tbsp of oil in a non-stick skillet on medium-high heat, and flip the buns into the skillet and remove the bowl. Cook for 3 to 5 minutes until golden brown on one side, flip, and cook about 3 to 5 minutes more till golden.
Mix the soy sauce, honey, Mirin and water in a sauce pan. Measure out cornstarch in a bowl and mix with a bit of the liquid mix to prevent clumping. Add back to the sauce mix. Cook at medium heat until it boils, and keep a boil going for about 1 minute. Cool for a bit.
Mix ground beef, half the teriyaki sauce, salt and pepper. Divide into 4 and make large patties. Heat a skillet at medium-high heat and add 1 Tbsp of oil. Cook the beef for 3-5 minutes on each side.
Build your burger
Place a patty on a ramen bun. Spoon some teriyaki sauce and mayonnaise. As you desire, place a slice of tomato, some lettuce, and chopped green onions. Top with another ramen bun. Enjoy!