Lightly grease 2 cookie sheets; set aside. In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking powder, and salt. Beat until combined, scraping sides of bowl occasionally. Beat in eggs and vanilla until combined. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour and lemon peel. Stir in pistachio nuts.
Divide dough into 3 equal portions. Shape each portion into an 8-inch roll. Place rolls at least 3 inches apart on prepared cookie sheets; flatten slightly until about 2-1/2 inches wide.
Bake in a 375 degree F oven for 20 to 25 minutes or until golden brown and tops are cracked (loaves will spread slightly). Cool on cookie sheet for 30 minutes.
Use a serrated knife to cut each roll diagonally into 1/2-inch slices. Place slices, cut sides down, on ungreased cookie sheets. Bake in a 325 degree F oven for 8 minutes. Turn slices over and bake for 8 to 10 minutes more or until dry and crisp (do not overbake). Transfer to a wire rack and let cool. Makes about 36 cookies.