These are about as far from Grandma's cucumber sandwiches as you're going to get. These babies will light up your spread with their fluorescent red and green color. Don't worry, there's nothing toxic here, it's just red horseradish, cucumber, scallion, and dill. The dill complements the cucumbers perfectly, and the scallions and horseradish give the sandwich some really good kick. My friends go through these things like water because they're so light and poppable. I've learned to make a double batch so I don't wind up back in the kitchen to make more of these during the party.
Peel the cucumber and slice it very, very thin. Lay the cucumber slices out on a sheet of paper towel and cover them with a second sheet. Let stand until the paper towels soak up the cucumber slices' liquid, about 15 minutes.
Mash the butter, scallions, dill, horseradish, salt and pepper together in a small bowl until well blended. Spread 5 of the bread slices with half of the dill butter, then top the butter with a layer of cucumber slices¿it's fine if they overlap a little bit. Spread the remaining butter over the remaining bread and top the sandwiches. Cut each sandwich into 4 pieces.