Sterilize the jars (See blog post for more instructions).
Wash the fruit and remove any bruised spots with a small knife. Remove the stone. Cut each peach into 6-8 wedges, cut the wedges into smaller pieces. Place in a large pot. Add lemon juice.
Bring the peaches to a boil on medium-low heat and simmer for 10 minutes until the pieces are softer.
Add sugar and star anise if using. Stir well for a couple of minutes until the sugar dissolves.
Cook on medium high heat for about 15-20 minutes until set. Stir every few minutes and make sure to scrape the bottom of the pot well when stirring to prevent the jam from catching.
Check if the jam is set. (Note 3)
Chunky jam: leave the preserves cool for about 10 minutes, this will allow the pieces to distribute more evenly. Transfer to jars and seal.
Smooth jam: blend the preserves with an immersion blender. Transfer to jars and seal.
Fill the jam into the sterilized jars using a funnel.
Can in water bath for 10 minutes, if desired, for longer shelf-life. Otherwise, keep the jars refrigerated or freeze them.