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Add the peach slices, lemon zest, lemon juice, and vanilla, into a heavy-bottomed large pot, over medium-low heat.
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Cook for about 15 minutes, until the peaches are soft, and the juices are released.
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Add the sugar, and stir into the mixture until dissolved.
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Increase heat to medium-high and bring the mixture to a boil, cook for 5 minutes, stirring continuously.
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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.
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Remove from heat, and let the jam cool completely before serving.
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Add them to mason jars and refrigerate.