Position a rack in middle of the oven and preheat to 350 degrees . Line 2 mini muffin pans with paper liners. In a medium bowl, whisk together the flour, baking powder and salt.
Using an electric mixer, beat 6 tablespoons butter and the granulated sugar on medium speed until fluffy. Beat in the egg and 2 teaspoons vanilla. With the mixer on low speed, beat in half of the flour mixture, followed by the milk. Beat in the remaining flour mixture until just combined.
Divide the batter among the muffin cups, filling each about two-thirds full. Bake until a toothpick inserted comes out clean, 13 to 15 minutes. Let cool in the pan for 5 minutes before transferring to a rack to cool completely.
Meanwhile, using an electric mixer, beat the remaining 1 stick butter on medium speed until fluffy. Gradually beat in the confectioners sugar, scraping down the bowl; stir in the remaining 1 teaspoon vanilla. Increase the speed to high and beat until light and fluffy, about 5 minutes. Frost the snack cakes with the buttercream and decorate with the sanding sugar.