Step 1: Prepare the egg salad by mixing the mashed hard-boiled eggs with mayonnaise, Dijon mustard, salt, and pepper until smooth. Set aside.
Step 2: Create the herbed cream cheese by whipping the softened cream cheese with fresh dill until well combined.
Step 3: Slice the English cucumber into very thin rounds. Place them on paper towels and lightly salt them for 10 minutes to remove excess moisture, then pat dry.
Step 4: Lay out all 12 slices of bread. Spread a very thin, even layer of softened butter on one side of each slice to prevent sogginess.
Step 5: For the Cucumber sandwiches: Layer cucumber slices on 4 buttered bread slices, sprinkle with mint, and top with 4 more buttered bread slices.
Step 6: For the Egg Salad sandwiches: Spread the egg mixture onto 2 buttered bread slices and top with 2 more buttered bread slices.
Step 7: For the Smoked Salmon sandwiches: Spread herbed cream cheese onto the remaining 2 buttered bread slices, top with smoked salmon, and cover with the final 2 buttered bread slices.
Step 8: Using a very sharp serrated knife, carefully cut the crusts off all the sandwiches.
Step 9: Cut the cucumber and salmon sandwiches into three long rectangles each, and the egg salad sandwiches into four small squares or triangles.
Step 10: Arrange on a serving platter and cover with a slightly damp paper towel until ready to serve to keep them fresh.