Hard boil eggs. Cool, peel, and chop; add to a mixing bowl.
Dice 1/2 the cucumber and add to the eggs, along with the mayonnaise, mustard, honey, salt, and pepper. Mix well. Spread the egg salad between each of 2 slices of bread, then cut into quarters.
Slice the remaining cucumber. Serve each sandwich with sliced cucumbers, cheese sticks, cherry tomatoes, and apples on the side.