Step 1In a standing mixer fitted with the paddle attachment or with a hand-held mixer, cream butter and sugar together until light and fluffy. Add the egg, vanilla and cider vinegar. Stir in the flour, baking powder and salt. Mix until combined. Turn out the dough, form into a ball, wrap with plastic film; refrigerate 30 minutes.
Step 2In a bowl, mix the egg white, white vinegar and 1 tablespoon water and set aside.
Step 3Place the chopped pistachios and sesame seeds in a wide dish or pie pan and set aside.
Step 4Heat the oven to 350 degrees. Divide dough in half; keep half reserved until ready to use. Measure 1 rounded teaspoon of dough, roll into a ball and flatten to form it into a 2-inch (by 1/8 -inch) circle. Lightly press one side of each cookie into the pistachios; turn the cookie over, brush the other side with egg wash and dip it in the sesame seeds to coat the other side. Place the cookies on a cookie sheet and bake pistachio-side down until the sesame seeds are lightly toasted and golden, 15 to 18 minutes.