If you are after a Moscow Mule riff that definitely has some kick, then you need to be making a Spicy Mule. It has the Vodka, Lime Juice and Ginger Beer of the original, but adds Cointreau and some slices of Jalapeño Pepper.
Thinly slice the Jalapeño and muddle a few slices with Lime Juice and Cointreau in a Collins glass. Add ice and Vodka, then top with Ginger Beer
Slice or two of Jalapeño