In a medium bowl, stir together the whipped cream cheese, thinly sliced green onions, minced fresh dill, and a pinch of sea salt and pepper until smooth and combined.
Lay out the brioche slices and spread a thin, even layer of the herb cream cheese on one side of each slice.
On half of the cream cheese–topped slices, layer thin cucumber slices to cover the surface.
Top the cucumbers with an even layer of thinly sliced smoked salmon, followed by a layer of thin radish slices.
Place a remaining cream cheese–coated slice of brioche on top to form a sandwich.
Using a sharp knife, trim crusts if desired and slice each sandwich into 4 small tea-sandwich pieces. Repeat with remaining ingredients until all sandwiches are assembled.
Arrange sandwiches on a platter and serve immediately.
