Preheat oven to 350°F (177°C) and grease a 9-inch springform pan.
Whisk flour, baking powder, baking soda, and salt in a bowl.
Beat 1/2 cup butter and sugar for 3 minutes until light and fluffy.
Add egg and vanilla, beating until smooth.
Mix in dry ingredients and milk on low speed until combined.
Pour batter into the pan and bake for 30-36 minutes until a toothpick comes out clean.
Cool the cake completely on a wire rack.
Crumble the cooled cake into fine crumbs in a large bowl.
Beat remaining butter, confectioners sugar, and a splash of milk to create a creamy frosting.
Mix frosting into cake crumbs until a dough-like consistency forms.
Roll the mixture into 24 uniform balls and chill in the refrigerator for 2 hours.
Melt candy wafers according to package instructions.
Dip a cake pop stick into the melted candy and insert into a chilled ball.
Dip the entire cake pop into the candy coating, allowing excess to drip off, then set on parchment to dry.