Preheat oven to 350º. Line a muffin pan with paper liners. In the bowl of an electric mixer fitted with the whisk attachment, mix the flour, sugar, baking powder, salt and malted milk powder. Switch to the paddle attachment. Add the root beer, eggs and vanilla to the bowl and mix on medium-high speed just until batter is thoroughly combined. Evenly divide batter between 12 muffin liners and bake for 18-20 minutes or until a toothpick inserted in the center of a cupcake comes out clean.
To make the frosting:
Combine butter and powdered sugar in the bowl of an electric mixer and beat on medium speed until smooth. Add root beer, one tablespoon at a time until your frosting reaches desired consistency.
To assemble the cupcakes, using a pastry brush, brush each cooled cupcake with root beer. Swirl or spread frosting on top. Sprinkle with coarse sugar, if desired.