Combine flour, lemon verbena leaves, baking powder, and salt; set aside. Beat butter in a large bowl with an electric mixer on medium speed for 30 seconds. Add sugar, eggs, and vanilla. Beat until well combined. Add half of the flour mixture. Beat until combined. Stir in remaining flour mixture with a wooden spoon until combined.
Drop dough by rounded teaspoonfuls 2 inches apart on an ungreased cookie sheet. Bake in a 350 degree F oven for 8 to 10 minutes or until edges are lightly browned. Remove to wire racks and cool. Makes 36.