Preheat your oven to 350°F. Fill a standard 12-cup muffin pan with liners.
Stir together the dark beer, vegetable oil, baking soda, sugar, and spices over medium heat. Allow them to cool after carefully heating them until boiling.
In a separate bowl, combine all of the remaining ingredients, leaving the eggs for last. Lastly, slowly add the eggs one at a time, gently mixing them.
Combine the two bowls of ingredients, gently mixing but not stirring.
Fill the cupcake liners evenly and bake at 350°F for 20-22 minutes.
Remove the cupcakes with the liners as soon as they come out of the oven. Allow them to cool entirely to room temperature.
Make the frosting by beating the butter at high speed in a stand mixer for 30 seconds.
Reduce the speed to low and gradually add half of the confectioner's sugar.
Again, beat them for 30 seconds at high speed.
Then, on low speed, add the lime juice, whole milk, and the remaining confectioner's sugar.
Continue beating them on high speed for 1-4 minutes, or until smooth and fluffy.
Fill a piping bag with frosting and decorate your cooled cupcakes as desired. After the frosting has been set, top each with some candied lime peel.
Unfrosted cupcakes can be stored in an airtight container at room temperature for up to a week, and frosted cupcakes for up to 5 days, but only in the fridge.