Bring the peaches, sugar, lemon juice, water, and salt to a low boil in a saucepan, and mash lightly with a potato masher until broken down into irregular chunks. Cook at a low boil for 4 to 5 minutes until reduced and saucy. (If it starts to become dry, you can add a splash more water.)
Remove from the heat. Stir in the vanilla and cinnamon. Taste and add additional sugar if desired. The sauce will thicken more as it cools. Serve immediately or refrigerate until serving. Store up to 1 week refrigerated or frozen for up to 3 months.