Boil eggs for 13–15 minutes until fully hard-boiled, then cool and peel.

Add eggs, mayonnaise, mustard, sugar, salt, and pepper to a food processor and blend until smooth.

Open the processor and mix any remaining uneven portions until fully uniform.

Spread filling onto bread slices, top with remaining slices, and gently press to settle.

Optionally trim crusts.

Slice sandwiches into triangles or rectangles, rinsing and wiping the knife between cuts to keep edges clean and moist.