Peel the cucumber and slice it into 1/8-inch rounds—this thin slicing is essential for even moisture removal and a delicate texture in the final sandwich. Place the sliced cucumbers in a fine-mesh strainer and toss with the kosher salt, which will draw out excess moisture and firm up the slices. Let them drain for 30 minutes to 1 hour; this step prevents your sandwich from becoming soggy and concentrates the cucumber flavor. I find that salting cucumbers ahead of time is the secret to keeping these delicate sandwiches from falling apart after a few hours.
While the cucumbers are draining, combine the softened cream cheese, mayonnaise, finely minced dill, finely minced chives, salt, freshly cracked black pepper, and lemon zest in a bowl. Mix until smooth and fully combined, ensuring the herbs are evenly distributed throughout for consistent flavor in each bite. The cream cheese should be at room temperature so it spreads smoothly without tearing the bread.
Once the cucumbers have fully drained, pat them dry with paper towels to remove any remaining moisture. Lay out 14 bread slices and spread 1 1/2 tablespoons of the cream cheese mixture from Step 2 on each slice. I like to use an offset spatula for even spreading—it ensures the filling reaches the edges and holds the cucumbers in place. Arrange approximately 15 drained cucumber slices on 7 of the prepared bread slices, then top each with a second bread slice, cream cheese side down, to create 7 sandwiches. Trim off the crusts with a sharp knife, then cut each sandwich diagonally in half or into triangles for a classic presentation.