Place quartered lime and sweetener (if using) in your copper mug or glass and gently muddle until the lime releases its juice. Don't press too hard or you'll make it bitter.
Clap mint leaves between your palms a few times to release their aroma, add to your mug, and press very gently just once or twice with your muddler.
If using alcohol-free vodka, pour it in now.
Fill your mug about three-quarters full with ice (crushed ice works best), then slowly pour in the ginger beer.
Give everything a gentle stir to combine all flavors without losing the fizz, garnish with a fresh mint sprig and lime wheel, and serve immediately while ice-cold.