In a large pitcher, combine the dry white wine and basil leaves. Use a wooden spoon or muddler to gently crush the basil leaves to release their flavor.
Add the sliced white peaches and honey to the pitcher, and stir until the honey is dissolved.
Cover the pitcher with plastic wrap and chill in the refrigerator for at least 1 hour (or up to 8 hours) to allow the flavors to meld together.
Just before serving, stir in the club soda to give the sangria some fizz.
Fill wine glasses with ice cubes, and pour the White Peach Basil Sangria over the ice. Garnish each glass with additional peach slices and basil leaves if desired.
If you prefer a sweeter sangria, you can add more honey to taste. And if you want to make this recipe non-alcoholic, you can substitute white grape juice or ginger ale for the white wine.