Whisk flour, baking powder, and salt in a bowl; set aside.

Cream butter and sugar until light, then beat in egg, vanilla, and pickle brine.

Gradually mix in dry ingredients until a soft dough forms; chill 30 minutes.

Preheat oven to 350°F (175°C). Roll dough into 1-inch balls, roll in sugar, and place on a lined baking sheet.

Bake 8–10 minutes until edges set but centers are soft; cool on a rack.