Add the chopped peaches, sugar (or honey), and 1 cup (240 ml) of the water to a medium saucepan. Bring to a gentle simmer over medium heat, stirring now and then to dissolve the sugar.
Once bubbling, lower the heat and cook for 8 to 10 minutes, until the peaches are very soft and the liquid smells strongly of fruit. Mash the peaches with a wooden spoon or muddler; for a smoother syrup, blend with an immersion blender. Remove from heat and cool a few minutes.
While the syrup simmers, bring 4 cups (950 ml) of water to just under a boil. Remove from heat, add the tea bags or loose tea, and steep for 4 to 5 minutes, no longer. Remove the tea bags or strain out the leaves without squeezing them.
Set a fine mesh strainer over your pitcher and pour the peach syrup through it, pressing the pulp gently with the back of a spoon to push through all the juice. Discard the solids.
Pour the hot brewed tea into the pitcher with the strained peach syrup. Add the lemon juice and stir well. Taste the concentrate; it should be a little strong and sweet since you will dilute it. Stir in the peach nectar now if using.
Add the remaining 3 cups (710 ml) of cold water and stir. Refrigerate for 30 to 60 minutes for the cleanest cold flavor, or serve straight away over plenty of ice.
Fill tall glasses with ice and pour the peach iced tea over the top. Garnish with fresh peach slices and a sprig of mint, then serve right away.