Wash the peaches thoroughly under cool running water.
Bring a large pot of water to a boil.
Carefully lower the peaches into the boiling water.
Blanch for 30 to 60 seconds, or until the skins begin to loosen.
Transfer the peaches to a bowl of cold water.
Peel away and discard the skins.
Cut each peach in half and remove the pit.
Chop the peach flesh into small pieces. You should have approximately 6 cups of prepared peaches.
Transfer the chopped peaches to a large, heavy-bottomed pot.
Add the granulated sugar, fresh lemon juice, and cinnamon stick.
Stir gently until the peaches are evenly coated.
Let the mixture rest for 15 to 20 minutes so the sugar begins dissolving in the peach juice.
Place the pot over medium-low heat.
Cook gently, stirring regularly, until the sugar dissolves completely.
When the mixture begins bubbling, reduce the heat to maintain a steady simmer.
Cook uncovered for 35 to 50 minutes.
Stir increasingly often as the mixture becomes thicker.
Remove any pale foam that rises to the surface.
Place a small spoonful of preserves on a chilled plate.
Let it cool for approximately 30 seconds.
Push it gently with your finger. It should appear thick and wrinkle slightly.
Continue cooking for another 3 to 5 minutes when the syrup is still too thin.
Remove and discard the cinnamon stick.
Gently mash a small portion of the peaches for a more spreadable consistency.
Spoon the hot preserves into clean, heat-safe jars.
Allow the jars to cool at room temperature.
Attach the lids and refrigerate once completely cooled.