For both the radishes and cucumbers, use a mandoline or sharp knife to thinly slice them crosswise, about 1/8-inch thick.

Place the sliced cucumber in a large fine-mesh strainer set over a bowl. Sprinkle with 1/2 teaspoon of the kosher salt and toss to combine. Let the cucumbers rest and drain, tossing occasionally, 30 minutes to 1 hour. This prevents soggy sandwiches.

Place cream cheese and Boursin cheese in a large food processor. Process until smooth. Add 1 teaspoon of olive oil (or more to reach the right smooth consistency) and process. Add dill, remaining 1/2 teaspoon Kosher salt and black pepper and pulse a few times to combine.

Using a small rubber spatula, offset spatula or back of a spoon, evenly spread 1-1/2 tablespoons of the cream cheese mixture onto 1 slice of the bread, leaving a 1/2-inch border; repeat with a second slice of bread. Shingle 6 to 8 slices of the cucumber and 3 to 4 slices of radish on top of one of the bread slices. Close the sandwich with the second slice of bread cream cheese side-down.

Repeat assembling until you have 8 whole sandwiches. Using a serrated knife, cut the crusts off all the sandwiches (these are for snacking!). Then quarter each sandwich to form smaller squares or triangles. Stack on a serving platter.

Wrap in plastic wrap (otherwise they dry out) and refrigerate. Sandwiches can be made a few hours in advance.