Juice lemons, strain and set aside the lemon juice.
Peel peaches, take out the pits, and slice them. Add peaches into a sauce pot and combine with sugar, vanilla extract, and 2 cups of water.
Stir and bring the mixture to simmer over medium heat. Lower the heat a little and let peaches cook until softened.
Pour the peach mixture into a pitcher through a strainer. You can add some of the peaches to the pitcher or all of them. Add remaining cold water to the pitcher and fresh squeezed lemon juice.
Stir everything together and refrigerate until cold.
Notes
You can adjust the amount of sugar to your taste, and add more lemon juice for extra tartness.