Heat a medium nonstick skillet over medium heat. Spread ½ tablespoon of the butter on 1 side of each slice of milk bread. Toast the bread slices butter-side down until golden brown, about 3 minutes.

Pan-fry the luncheon meat in the same nonstick skillet over medium heat until browned and crisp on the bottom, about 3 minutes. Flip and repeat until golden brown and crisp on the other side, about 3 minutes. Arrange 2 slices of meat on the toasted side of 2 slices of bread.

Meanwhile, divide the cornstarch between 2 small bowls, add 1 tablespoon cold water to each bowl and whisk until the cornstarch is dissolved. Divide the sugar, eggs and bouillon powder, if using, between the bowls and whisk briefly to combine. Then add 1 teaspoon oil and ¼ teaspoon salt to each bowl and continue to whisk until no streaks of egg whites remain, about 30 seconds.

Heat 1 teaspoon neutral oil in the same nonstick skillet until it just starts to smoke. Remove from the heat, add the egg mixture from 1 bowl and slowly gather the cooked eggs as they form into the center using a heatproof spatula and shape to the size of the milk bread. Transfer the eggs to 1 of the meat-topped bread slices. Add the remaining 1 teaspoon neutral oil to the skillet and repeat with the egg mixture from the second bowl, topping the second meat-topped bread slice with the cooked eggs.

Top the sandwiches with the remaining milk bread slices toasted-side down.