Peel the peach, remove the pit, and roughly chop it. Add the pieces to a blender and puree until smooth. (If the puree is too thick, add 1 tablespoon f water to help thin it out.)
Spoon half peach puree (about 2-3 tablespoons) into the bottom of a Collins glass. Repeat with the other glass. Fill the glasses with ice.
Pour 2 ounces of vodka into each glass. Fill each glass the rest of the way with ginger beer.
Squeeze a wedge of lime into each glass. Garnish with a peach slice and/or lime slice on the rim if desired. Serve immediately.