In bowl of electric mixer, cream butter and sugar on medium speed for 5 minutes, until light and fluffy. Beat in egg and vanilla. Mix flour, baking powder, and salt in large bowl. Gradually add to butter mixture, beating on low speed, until combined. Gradually add milk, beating constantly until smooth and well combined.
Roll out dough to a thickness of 1½cm (½in) on a lightly floured work surface. Using a cookie cutter, cut into round discs.
Scoop small mounds of chopped pistachios (about ½ teaspoon each) onto a baking sheet, spacing them apart. Place a dough discover nuts, pressing down so nuts adhere to disc bottoms. Brush discs with egg white, then sprinkle generously with sesame seeds to cover.
Bake on middle rack of oven for 15 minutes, or until golden brown.
