In a medium bowl, beat butter or margarine and brown sugar with an electric mixer on medium speed until light and fluffy. Beat in lemon zest, lemon extract, and vanilla.
Add flour and salt to butter/sugar mixture and blend well. With a rolling pin on a lightly floured surface, roll out dough 1/4 inch thick. Cut out cookies using a 2 inch round cutter and place 2 inches apart on ungreased cookie sheets. Reroll scraps.
Bake 20 to 25 minutes, until cookies are pale golden, not brown. Let stand 2 minutes. Remove to a rack and let cool completely.