Heat oven to 350°F. Line two baking sheets with parchment.
Whisk flour, baking soda, baking powder, and salt in a bowl.
Cream butter, peanut butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the egg and vanilla until smooth.
Mix in the dry ingredients just until combined. Add the milk only if the dough feels dry.
Scoop dough into 1-tablespoon portions and roll into balls.
Roll each ball in granulated sugar, then coat generously in powdered sugar.
Arrange on prepared sheets, spacing about 2 inches apart.
Bake 9–11 minutes, until tops crack and edges look set but centers are soft.
Cool on the sheet 5 minutes, then move to a rack to finish cooling.