Wash the peaches thoroughly and slice them into thin pieces. There's no need to peel them because the skins contribute additional color and flavor. Set aside a few slices for garnish later.
Add sugar, water, and sliced peaches to a small saucepan. Bring the mixture to a gentle boil, then reduce the heat and lightly mash the peaches with a spoon to release their juices and flavor.
Once the sugar has fully dissolved, remove the pan from the heat. Cover it and allow the peaches to steep in the syrup for about 25 to 30 minutes so the flavor becomes concentrated and aromatic.
While the syrup is steeping, brew the black tea in hot water. Allow the tea to steep for about 4 to 5 minutes, then remove the tea bags or strain out the loose leaves to prevent bitterness.
Transfer the brewed tea to a large pitcher. Place it in the refrigerator until it becomes cool and refreshing. Chilling the tea before mixing helps maintain a clean flavor.
Pour the peach syrup through a fine-mesh strainer into a clean container. Press lightly on the peaches to extract as much flavorful syrup as possible without forcing pulp through the strainer.
Add the desired amount of peach syrup to the chilled tea and stir well. You can also keep the syrup separate and allow everyone to sweeten their own glass according to taste.
Fill serving glasses with ice cubes and fresh peach slices. Pour the peach iced tea over the ice and serve immediately for the most refreshing experience.