These cupcakes hit on all the classic notes of a Moscow Mule. It starts with a buttery vanilla cake that's loaded with dried and crystallized ginger and is finished with a simple lime syrup. The cupcakes are also topped with a vanilla and lime buttercream, which you can optionally spike with vodka. For the full Moscow Mule effect, use copper-colored liners.
Make the cupcakes: Preheat the oven to 350˚ F. Line a 12-cup muffin tin with foil or paper liners. Whisk the flour, ground ginger, baking powder and salt in a medium bowl. In a large bowl, beat the butter, 1 cup granulated sugar and the crystallized ginger with a mixer on medium-high speed until light and fluffy, 4 to 5 minutes. Beat in the eggs, one at a time, then the vanilla. Reduce the mixer speed to low and beat in the flour mixture in three additions, alternating with the milk in two additions, until combined.
Divide the batter evenly among the muffin cups, filling them about two-thirds of the way. Bake until the cupcakes are golden brown and the centers spring back when gently pressed, 20 to 25 minutes. Let cool 5 minutes in the pan. Meanwhile, combine the remaining 2 tablespoons granulated sugar and the 2 tablespoons lime juice in a small bowl and stir to dissolve the sugar. Remove the cupcakes to a rack, brush the tops with the lime-sugar mixture and let cool completely.
Meanwhile, make the frosting: Beat the butter and lime zest in a large bowl with a mixer on medium-high speed until smooth and creamy, about 2 minutes. Add the vanilla, confectioners' sugar and salt and beat on low speed until combined, then increase the speed to medium high and beat until light and fluffy, about 3 minutes. Add the milk, lime juice and vodka (or more milk) and continue beating until well incorporated, about 1 more minute. Transfer to a piping bag fitted with a 1/2-inch round tip and pipe on the cupcakes. Garnish each with a lime slice.