Preheat the oven to 350 degrees F.
Lay the pistachios on a cookie sheet in a single layer. Bake for 10 minutes or until the nuts are lightly toasted. Remove from the oven.
In an electric mixer, beat the butter until light and fluffy. With the mixer running, gradually add the eggs, sugar, and vanilla; mix until creamed. Add the flour, baking powder, and salt. Mix the dough until smooth. Using a wooden spoon, mix in the pistachios until evenly distributed.
Put the dough on a lightly floured surface and cut in half. Roll each half into a log, each 12 inches long by 1-inch high. Place the logs on an ungreased cookie sheet and bake for 35 minutes or until the bottoms are lightly brown. Let the logs cool for 5 minutes and then place on a cutting board. Slice each log on a diagonal into 12 1-inch thick pieces. Put the cookies back on the cookie sheet and bake 5 minutes. Turn the cookies over and bake the other side for another 5 minutes. Store cookies in an airtight container.