Fill a large bowl with ice water to create an ice bath.

Bring a medium saucepan of water to a rolling boil over high heat. Carefully lower in the eggs using a slotted spoon. For medium soft-boiled eggs, boil for 7 minutes, then turn off the heat and let them sit for 1 minute. For hard-boiled eggs, boil for 10 minutes until fully cooked.

Once the eggs are boiled to your desired doneness, transfer them immediately to the ice bath. Let the eggs cool for about 2 minutes.

Place the peeled eggs in a mixing bowl and mash them with a fork until they reach a chunky consistency. Add sugar, salt, pepper, and mayonnaise. Mix until creamy.

Lay out your slices of Japanese milk bread. Spread softened butter on one side of each slice. Place a scoop of egg salad between two slices, pressing gently to secure.

Cut the assembled sandwiches in half for easier handling. Serve immediately or wrap securely in plastic wrap for storage.