In a large bowl, cream together the sugar and butter until smooth. Beat in the egg, then stir in the vanilla and zucchini.
Combine the flour, baking soda, cinnamon, and salt; stir into the zucchini mixture. Mix in nuts if desired. Drop by spoonfuls onto ungreased baking sheets.
Bake for 10 to 15 minutes, or until edges are golden. Remove from oven and let cool on wire racks.
Notes:
These cookies are a great way to use up extra zucchini from the garden.