Make simple syrup by heating sugar and water in a small pot until sugar dissolves. Let the syrup cool after removing it from the heat.
Squeeze lemons and strain juice to remove pulp and seeds.
Pour the vodka into the pitcher.
Add fresh lemon juice and the cooled simple syrup.
Pour in cold water and stir well.
Chill the mixture for at least 1 hour before serving.
Fill glasses with ice cubes.
Pour the cocktail mixture into glasses.
Garnish with lemon slices and mint sprigs if desired.
Notes
Store any leftover simple syrup in an airtight container in the fridge for up to 2 weeks.The recipe serves 8-10 people and can be doubled for larger groups.Make a non-alcoholic version by replacing vodka with extra cold water or club soda.Use fresh lemons rather than bottled juice for the best taste.Keep the cocktail cold by adding frozen lemon slices instead of regular ice cubes to prevent dilution.