Add the softened cream cheese to a mixing bowl.
Stir in the lemon zest and chopped dill until evenly combined.
Lay four slices of bread flat on a cutting board.
Spread the cream cheese mixture evenly over each slice.
Arrange the smoked salmon in a thin, even layer on top of the cream cheese.
Place the remaining bread slices on top to form sandwiches.
Press gently to secure the layers.
Wrap the sandwiches tightly in plastic wrap or place in an airtight container.
Refrigerate for at least 1 hour before slicing and serving.