Chop dill and green onion finely. Mix with the softened cream cheese, salt, and pepper to taste. Set aside.
Peel the cucumbers. Cut into very thin slices (Note). Pat the pieces a bit dry with kitchen paper (especially if using an English cucumber).
Spread cream cheese on the tortillas. Cover with cucumbers, overlapping them a little to make them fit.
Roll up tightly. Wrap in plastic wrap and refrigerate for about 30 minutes to allow the cheese to set slightly.
Remove the plastic wrap. Use as many toothpicks or wooden picks as needed to secure the roll-ups; it depends on the desired thickness of the pieces. I cut 7 pieces out of each tortilla, so I had 21 in the end. Use a serrated knife to slice the roll between the picks.
Arrange on a platter and garnish with a few fresh dill sprigs (optional).
I prefer to use a mandolin; the slices will be perfectly thin and regular.