Over medium heat, mix water and powdered erythritol until dissolved.
Add mint leaves and bring to a boil.
Once boiling, bring heat down to a simmer and steep for 5 minutes.
Remove from heat and allow mixture to cool. If you want the syrup sweeter, add stevia. Test it first...I usually don't add the stevia however I prefer this less sweet.
Once simple syrup is cool, combine mint-infused syrup, vodka, lime juice and club soda in a pitcher.
Serve in ice filled glasses with some muddled mint leaves at the bottom (place fresh mint in the bottom of the glass and use a cocktail muddler--or a spoon---to crush the leaves and release it's essence). Garnish with lime and extra mint sprigs.