In a small bowl, stir together cream cheese, mint, lemon zest and juice, and salt.
Using a vegetable peeler, shave 15 (5x1 ¼-inch) lengthwise strips from cucumber.
Using a rolling pin, roll white bread slices to a ¼-inch thickness. Divide cream cheese mixture among bread slices. Spread cream cheese into a thin, even layer over bread slices. Starting on one long side, shingle 5 cucumber slices on top of cream cheese, trimming as necessary. Starting on a long end, roll up bread jellyroll style to encase cucumber and cream cheese. Wrap each log tightly in plastic wrap and refrigerate for at least an hour.
Just before serving, unwrap logs and place on a cutting surface. Using a thin, serrated bread knife in a gentle sawing motion, trim and discard ends to make 5-inch-long logs. Cut each log into 5 (1-inch) slices. Serve immediately.
Recipe by TeaTime Magazine at https://teatimemagazine.com/cucumber-mint-cream-cheese-pinwheels/