Dice peaches, leaving the peels on.

Add the diced peaches, lime juice, and corn syrup into the food processor. Puree until there are no large chunks.

Strain into a large bowl through a fine mesh strainer. Add the salt to taste. Press plastic wrap against the surface and chill in the refrigerator until very cold (at least 3 hours).

Churn in your ice cream maker according to manufacturer's instructions. I use the kitchen aid ice cream maker attachment and churn for about 20 minutes. Transfer to an airtight freezer container (I like to use these, a bread pan with saran wrap also works in a pinch.) Freeze for 2-3 hours, until the desired consistency is reached.

Add the water to a small saucepan and bring to a boil over medium-high heat. Once it comes to a boil, remove from the heat and add the tea bags. Let steep 5 minutes, then remove the tea bags and discard.

Add the sugar and stir until completely dissolved. Put in a pitcher and add another 4 cups of water.

Refrigerate until chilled.

Fill a pint glass or wide-mouth mason jar with 2-3 scoops of peach sorbet. Pour sweet tea over the top until the glass is almost full. Add a straw and enjoy immediately, preferably while swinging on a porch.