First, ensure your butter is properly softened but not melted. In a large bowl, cream the softened butter until it is completely smooth. Add ½ cup of the confectioners' sugar and beat the mixture with an electric mixer until it becomes light and fluffy. Finally, mix in the pure vanilla extract until it's fully combined.
In a separate medium-sized bowl, whisk together the all-purpose flour, the entire package of instant pistachio pudding mix, and the salt. Gradually add this dry mixture to your wet butter mixture, mixing on low speed until the dough just comes together. Be careful not to overmix at this stage.
Divide the finished dough into two equal portions. Shape each portion into a flat disc and wrap it tightly in plastic wrap. Refrigerating the dough is a critical step; chill it for at least one hour. This helps the cookies hold their shape during baking and prevents them from spreading too much.
Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper to prevent sticking. Once chilled, take the dough and form teaspoon-sized balls. Place them about one inch apart on the prepared baking sheets. Gently flatten each ball slightly with your palm or the bottom of a glass before baking.
Bake the cookies for 9–10 minutes. They will be soft and should not look brown. Let the cookies rest on the baking sheet for about five minutes after taking them out of the oven. While they are still warm, gently roll each one in the remaining ½ cup of confectioners’ sugar. Place them on a wire rack to cool completely.