Make sure your ice cream maker is ready to use. Freeze any part necessary.
In a good sized pot over medium heat, stir together the sugar and water until the sugar has dissolved.
Add the peaches and salt, and stir to combine. Let simmer for 15-20 minutes, or until the peaches have softened and started to disintegrate slightly (this can vary depending on the ripeness of your peaches).
Turn off the heat, and either transfer in small batches (CAREFULLY) to a blender/food processor, or do as I did and use your immersion blender right in the pot and puree until smooth.
Add the thyme sprigs to the mixture and let cool in the fridge, overnight if possible.
When the peach goodness is as cold as can be, remove the thyme, and stir in the lime juice and vodka. Pour into your ice cream maker and process according to your machine’s directions.
Pour the frozen sorbet into a freezer safe container and let freeze until hardened, at least 4 hours.