Sift the flour, baking powder, custard powder, and salt in a separate bowl.
Set it aside.
Add the sugar and the butter to the bowl of your stand mixer.
Mix it with a balloon whisk on medium speed until creamy, light, and fluffy. Scrape down the sides and bottom of the bowl as needed.
Now add the sifted dry ingredients to the wet ingredients and add the pistachio essence and chopped pistachios. Mix it well.
The cookie mixture will become crumbly and look like breadcrumbs.
Gradually add milk to this mix and knead it until it forms a soft, pliable dough. Add milk sparingly as it is only required to bind the dough. More of it will turn the dough wet and sticky. So, a little vigilance while adding it will be necessary.
Cover the eggless pistachio cookie dough with plastic wrap and chill in the refrigerator for 1- 2 hours or overnight. Do not omit this step.
Preheat the oven to 350°F. Unwrap the dough and cut each dough log into ¼-inch-thick slices.
Place the sliced cookies 1¼-inch apart onto a greased baking tray.
Bake the cookies for 12-15 minutes. Once the cooking time has elapsed, remove the tray from the hot oven and allow the cookies to cool completely.
Transfer the cooled cookies into an airtight container or a sealed jar and store them.