Start by peeling the peaches. You can do this by blanching them in boiling water for about 30 seconds and then immediately transferring them to an ice bath. The skins should easily peel off. Once peeled, slice the peaches into wedges or desired shape.
In a mixing bowl, combine the peach slices, lemon juice, vanilla extract, and ground cinnamon. Gently toss the peaches to coat them evenly with the lemon juice and spices. Let the mixture sit for about 10 minutes to allow the flavors to meld.
In a small bowl, whisk together the cornstarch or arrowroot powder and unsweetened apple juice or water until smooth. This mixture will act as a natural thickener for the peach filling.
Reduce the heat to low and allow the peach mixture to simmer gently. Stir occasionally until the filling thickens and coats the back of a spoon. This process usually takes about 5-7 minutes. Keep a close eye on it to prevent scorching.