Using an offset spatula or the back of a spoon, gently spread the dill cream cheese in a thin, even layer over the entire surface of the salmon sheet. Leave a narrow 1/2-inch strip bare along one long edge; this will help seal the roll without excess filling squeezing out.
Lay the cucumber matchsticks in a single, loose line along the opposite long edge (the one that is fully covered with cream cheese). You want just a modest row—too many cucumbers will make the roll difficult to slice cleanly.
Starting from the long edge with the cucumber, roll the salmon up tightly into a log, using the parchment or plastic wrap underneath to help you lift and roll while keeping it snug. As you reach the bare edge, press gently so the cream cheese seals the seam.
Wrap the salmon log firmly in the parchment or plastic wrap, twisting the ends like a candy wrapper to tighten the roll. Refrigerate for at least 30–45 minutes, or up to 4 hours, to allow the cream cheese to firm up and the pinwheels to slice cleanly.
When ready to serve, unwrap the chilled salmon log and place it on a cutting board. Using a very sharp knife, trim off a thin slice from each end for a cleaner look (cook’s treat), then slice the log into 1/2-inch rounds, wiping the knife with a damp cloth between cuts to keep the spirals neat.
Arrange the smoked salmon pinwheels cut-side up on a white plate or platter so the pink-and-white spiral pattern is visible. Sprinkle lightly with a bit of extra fresh dill for color, and serve immediately while still cool.
