Lay the slices of bread out on a parchment-lined baking sheet and freeze for at least one hour. This will make slicing the sandwiches with clean edges a lot easier.
Prepare the dilly cream cheese dip. Add the cream cheese, dried dill, garlic powder, salt, pepper, lemon juice, and sliced green onion to a bowl. Whip the ingredients together with a spoon until everything is evenly mixed and the cream cheese is soft and spreadable.
When you're ready to make the sandwiches, peel the cucumber if desired, then slice it very thinly. I just use a knife to carefully slice the cucumber. You can also use a mandoline slicer using the ⅛-inch setting (3mm).
Take two slices of bread out of the freezer at a time and spread about 1.5 Tbsp cream cheese over the surface of each piece of bread, from edge to edge. Layer the slices over one piece of bread, then top with the other slice (cream cheese side facing the cucumbers).
Carefully slice the crusts off the bread, then cut the sandwich into two or four pieces (four small pieces is great for finger foods or party appetizers). Repeat until all the sandwiches are assembled. If you have any leftover cucumber slices, place them on top as garnish. Serve within 1-2 hours of assembly.
*I use dried dill here because it's easy to keep on hand, and you only need a small amount. It's also more affordable than fresh because it's shelf-stable. If you'd prefer to use fresh dill, use 1½ tsp fresh chopped dill in place of the ½ tsp dried dill.**English cucumbers work best because they have thin skin and small, soft seeds. You can leave the skin on, peel it, or partially peel for color. You can use regular cucumbers, but I recommend peeling them to remove the tougher skin.Mayonnaise: For a creamy spread, add 1-2 Tbsp of mayonnaise to the mix. I'd start with just 1 Tbsp, since too much can make the filling loose and the bread soggy.