Combine the peeled, pitted, and sliced peaches with the cane sugar in a food processor. Blend until completely smooth, about 1-2 minutes, scraping down the sides as needed to ensure even processing. The sugar will begin breaking down the peaches and releasing their juices, creating a smooth purée. Transfer this mixture to a bowl.

Stir the lemon juice, sea salt, and vanilla extract into the peach purée from Step 1 until fully incorporated. The lemon juice brightens the peach flavor and prevents the sorbet from tasting one-dimensional, while the salt enhances the natural sweetness. I like to taste at this point and adjust the lemon juice if needed—different peaches have varying acidity levels, so a touch more or less can make a difference in the final result.

Pour the sorbet base into a shallow container or baking dish and cover tightly with plastic wrap or a lid. Freeze for 6-7 hours until the mixture is completely firm. For the smoothest texture, I recommend stirring the mixture every 2 hours during the first 4 hours of freezing to break up ice crystals as they form, creating a more scoopable consistency rather than a solid block.