Place a small plate in the freezer before you start cooking.
Wash the peaches thoroughly.
Bring a large pot of water to a boil. Prepare a large bowl filled with ice water just before the water starts boiling.
Carefully add the peaches to the boiling water.
Using a slotted spoon, remove the peaches after 30 seconds and immediately transfer them to the ice bath.
Once the peaches have cooled, take them out of the ice bath and gently peel away the skins using your hands.
Remove the pits and cut the peaches into fourths or eighths, about 3/4” chunks.
In a medium or large saucepan, combine the peach chunks, sugar or honey (1/3 cup for a lightly sweetened version or 1/2 cup for a more traditional sweetness), and lemon juice. Mash about half of the peaches with a potato masher.
Bring to a boil over medium-high heat, stirring frequently. Once it starts boiling, reduce the heat to maintain a full boil.
Boil for about 12 minutes, reducing the heat if necessary to prevent burning, until it reaches 220°F for the sugar version or 227°F for the honey version. It will be slightly runny but will thicken as it cools and more as it’s chilled. From the time you add the peaches to the pan until they are done, it should take about 21 minutes total.
To test if the jam is ready, drop a small spoonful onto the cold plate and let it sit for a minute. Push it with your finger - if it wrinkles and holds its shape, the jam is done.
Remove the saucepan from heat and let it cool completely on a wire rack for about 2 hours. Then refrigerate in an airtight container.
This recipe yields about 1 1/3 cups of jam. Transfer into clean jars and refrigerate for up to 1 week. The jam can also be frozen for up to 1 year.