Steps

1. Bring a pot of water to a boil.
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2. Add salt 1/2 tsp to the boiling water.
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3. Gently place 3 eggs, taken out from the refrigerator about 10 minutes prior, into the pot and boil for 12 minutes.
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4. Remove the boiled eggs from the heat and immediately cool them in ice water for about 10 minutes. [This is the secret!] Cooling in ice water immediately after boiling makes the shells easier to peel. Be sure to use ice water, not just cold water.
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5. Peel the shells off the cooled eggs. Make a crack on the round side, peel along with the thin membrane, and gently rub with the pad of your thumb while immersed in water for a clean peel.
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6. Cut the eggs in half, place the yolks in a separate bowl, and chop the egg whites into approximately 1cm cubes. [This is the secret!] Chopping the egg whites coarsely adds more satisfying texture.
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7. Mash the egg yolks in the bowl until smooth using a rubber spatula (a masher or fork also works), creating a creamy consistency. [This is the secret!] Creaming the egg yolks results in a rich and creamy egg sandwich filling.
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8. Add mayonnaise 3 tbsp, sugar 1/2 tsp, and salt a pinch to the mashed yolks and mix thoroughly for about 1 minute. [This is the secret!] Thoroughly mixing for 1 minute makes the cream even smoother.
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9. Add vinegar 1/2 tsp to the bowl from step 5 and mix well. [This is the secret!] Adding vinegar creates a light yet rich flavor. Sugar is added to enhance the richness.
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10. Add the chopped egg whites to the bowl from step 6 and gently mix to combine. Taste and adjust sweetness and saltiness to your preference.
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11. Spread 10g of salted butter evenly on the inner sides of 4 slices of bread (8-slice thickness). [This is the secret!] Buttering enhances the flavor and prevents the moisture from the filling from soaking into the bread. Using mustard butter is also recommended.
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12. Place 4 slices of ham on the buttered bread, spread half of the egg filling, place another 4 slices of ham on top, and sandwich with bread. Lightly press with your hands.
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13. Tightly wrap the sandwiches with plastic wrap without any gaps and let them rest for about 10 minutes. Make another set in the same way. [This is the secret!] If it's hot during the day, let them rest in the vegetable crisper drawer. Wrapping in plastic wrap prevents them from falling apart.
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14. While still wrapped in plastic wrap, trim off the crusts of the bread. Remove the plastic wrap, cut diagonally, and serve. [This is the secret!] Cutting while wrapped in plastic wrap prevents the bread from shifting and allows for a clean cut. Be careful not to include any scraps of plastic wrap.
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15. Cut the leftover bread crusts into three equal pieces.
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16. Arrange the cut bread crusts in a heatproof dish without overlapping, cover with plastic wrap, and microwave at 600W for 3 minutes.
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17. Remove, flip over, and microwave for another 30 seconds at 600W. They should be crisp all over.
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18. In a frying pan, combine 30g of sugar and 2 tsp of water and let the sugar soak up the water.
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19. Heat over medium heat and cook without stirring until the edges start to color.
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20. Once slightly colored, lift the pan to distribute the heat and continue cooking until just before a good caramel color is achieved. Turn on the ventilation fan and shake the pan occasionally while cooking. [This is the secret!] Do not stir until the color changes, or the sugar will crystallize.
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21. Once caramelized, reduce heat to low, turn off the heat, and add 25g of salted butter to melt.
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22. Once the butter has melted, add the bread crusts and coat them thoroughly.
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23. Continue to stir in the frying pan with the heat off until the bread crusts separate and are coated.
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24. Transfer to a container lined with parchment paper, spread them out so they don't stick together, and let cool completely to finish.
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