In a stand mixer or with a hand mixer, beat the butter, oil and sugar together until light and white and fluffy
Add the cornstarch-water mixture, baking powder, salt, vanilla extract and blend well until mixture is smooth.
Add flour, cardamom powder and pistachio powder and mix.
Roll into small balls, about 1-inch in diameter, and place on a greased cookie sheet, one inch apart. Press down slightly to form discs. Press a pistachio, whole or half, into the center of each cookie.
Bake in a 350-degree oven for about 11-12 minutes, rotating the sheet halfway through the baking. Remove when the cookies have a hint of golden-brown color on top.
Place the baking sheet on a rack and let the cookies cool completely before removing them gently with a ladle.