Slice your cucumber in half lengthwise. This gives the cucumbers a flat, stable surface for further cutting.
With the flat side of the cucumber flat against the cutting board, use a potato peeler to thinly slice the cucumbers lengthwise into long strips of cucumber. Continue slicing until there is no cucumber remaining.
Lay the cucumber strips vertically, overlapping them ⅓ to half the width on each side.
Dry with a paper towel or clean dish towel.
Cut the bed of cucumber stips in half horizontally. You now have two beds of cucumber strips. (These will become two cucumber rolls).
At the base of the cucumber bed, spread softened cream cheese. Then add shredded carrots, salmon, and avocado.
Starting from the base, vertically roll up the ingredients into one long sushi roll.
Repeat steps 6 and 7 for the other bed of cucumber stirps.
Slice into classic sushi roll bites, and garnish with toasted sesame seeds. Serve with sauce.