Add peaches to a blender and puree until smooth. Set aside.
Set out two copper mugs (or cocktail glasses). Add 3 mint leaves and 1 lime wheel to each mug. Gently muddle.
Fill the glasses with ice.
Divide the peach puree between the two mugs, along with 2 oz vodka each. Stir to combine.
Top with ginger beer, stirring briefly.
Garnish with mint, peach, and lime.