Chiffonade Cut
Chiffonade (Little Ribbons in French) is exactly what you will be wanting to achieve with this cut.
This cut would be used in cutting herbs such as parsley, coriander, mint etc as a garnish and leafy vegetables such as lettuce, cabbage and greens.
The technique involves stacking the leaves in a little pile (in the case of herbs, remove the leaves from the stems first), roll them into a cigar shape that is nice and tight and then very finely slice(not chop) the leaves so they resemble thin ribbons