In a medium bowl, combine the whipped cream cheese, thinly sliced green onions, minced dill, and a pinch of sea salt and pepper; stir until smooth and evenly mixed.
Lay out two slices of brioche bread and spread a thin, even layer of the herb cream cheese on one side of each slice.
On one prepared slice, arrange a single layer of thin cucumber slices to cover the surface.
Top the cucumbers with an even layer of thinly sliced smoked salmon, covering the cucumber.
Add a layer of thin radish slices over the salmon.
Place the second slice of bread, cream cheese side down, to form a sandwich. Press gently to adhere.
Using a sharp knife, trim crusts if any remain and slice each sandwich into 4 small tea sandwiches. Repeat with remaining bread and fillings to make a total of 10 sandwiches.