Add the peach slices, lemon zest, lemon juice, and vanilla, into a heavy-bottomed large pot, over medium-low heat.
Cook for about 15 minutes, until the peaches are soft, and the juices are released.
Add the sugar, and stir into the mixture until dissolved.
Increase heat to medium-high and bring the mixture to a boil, cook for 5 minutes, stirring continuously.
After the 5 minutes, reduce the heat to low-medium, and slowly cook for another 40-60 minutes, not boiling. The jam is ready when the mixture is thick enough to leave a trail behind the spoon.
Remove from heat, and let the jam cool completely before serving.
Add them to mason jars and refrigerate.