Prep the vegetables: Wash the cucumber and radishes well. Pat dry.
Using a mandoline or a sharp knife, slice them as thinly as you can. Place slices on a paper towel-lined tray and lightly sprinkle with a pinch of salt. Let them rest 10 minutes to draw out excess moisture, then blot gently.
Make the chive butter: In a bowl, combine the softened butter, chopped chives, lemon juice, 1/4 teaspoon salt, and a few grinds of pepper.
Mix until smooth and evenly green-streaked. Taste and adjust seasoning. The butter should be savory, lightly tangy, and full of chive flavor.
Prepare the bread: Lay out the bread slices.
If you prefer a classic tea look, trim the crusts with a sharp serrated knife. Save the crusts for breadcrumbs or snacking.
Spread the butter: Gently spread a thin, even layer of chive butter on one side of every slice. Don’t skimp—this layer acts as flavor and as a moisture barrier to keep the bread from getting soggy.
Layer the cucumbers: On half of the buttered slices, shingle cucumber slices in a single, overlapping layer.
Aim for full coverage but avoid thick piling. Add a tiny sprinkle of pepper if you like.
Add the radishes: Arrange a neat layer of radish slices over the cucumbers. Keep it even so the sandwiches cut cleanly and bite easily.
Close the sandwiches: Top with the remaining buttered bread slices, buttered side down.
Press very gently to set.
Chill briefly (optional): For the cleanest cuts, place the sandwiches on a tray and chill 10–15 minutes. This helps the butter firm up and keeps layers tidy.
Cut to serve: Use a sharp serrated knife to slice into neat fingers, triangles, or squares. Wipe the blade between cuts for a clean look.
Finish with a tiny pinch of flaky salt on top, if using.
Serve: Arrange on a platter. They’re best slightly cool, not ice cold, so the butter softens and the flavors bloom.