Preheat oven to 325°F (165°C) and line two baking sheets with parchment.
Ensure butter is at room temperature for proper creaming.
Beat butter and powdered sugar until light and fluffy, about 3–4 minutes.
Add vanilla and mix until incorporated.
Whisk flour and potato starch in a separate bowl.
Gradually mix dry ingredients into the butter mixture until just combined.
Roll dough into 1-inch balls and place 2 inches apart on baking sheets.
Lightly flatten each cookie with a fork using a crosshatch pattern.
Bake for 12–15 minutes until just set but still pale.
Cool on baking sheet for 5 minutes, then transfer to a wire rack.