Using a serrated bread knife, trim and discard crusts from bread slices. Cut each bread slice into 3 (3x1¼-inch) rectangles. Cut 9 (3x1¼-inch) rectangles from ham slices.
Spread a thin layer of aïoli onto each bread rectangle. Top each bread rectangle with a ham rectangle, and shingle 3 cucumber pieces atop ham.
Serve immediately, or cover with damp paper towels, place in a covered container, and refrigerate until serving time, up to 30 hour.
Notes
*A mandoline is essential for cutting paper-thin slices of cucumber. For testing purposes, we used a Kyocera mandoline, available at Sur la Table.
Recipe by TeaTime Magazine at https://teatimemagazine.com/cucumber-ham-canapes-recipe/