Prepare a canning pot and four half pint jars.
Combine the prepped peaches, sugar, cardamom and lemon juice in a low, wide, non-reactive pot and stir to combine.
Once the sugar has started to dissolve and there's some liquid in the pot, place it on the stove over high heat and bring to a boil. Reduce the heat to medium-high and cook, stirring regularly for 15-20 minutes, until the total volume in the pot has reduced by at least one-third and the jam looks quite thick.
As the jam cooks, use a potato masher to help break down the peaches.
Funnel the jam into the prepared jars, leaving 1/2 inch headspace.
Wipe the rims, apply the lids and rings, and process in a boiling water bath canner for 10 minutes.
When the time is up, remove the jars and set them on a folded kitchen towel to cool.
Once the jars have cooled enough that you can comfortably handle them, check the seals. Sealed jars can be stored at room temperature for up to a year. Any unsealed jars should be refrigerated and used promptly.