Prepare a boiling water bath canner and enough jars to hold 6 pints of jam.
Pour the peaches into a large, non-reactive pot.
Whisk the pectin, cinnamon, and nutmeg into the sugar to combine and add that to the fruit.
Stir so that the peaches begin to release their juice and the sugar begins to dissolve.
Bring to a boil over high heat and cook, stirring regularly for 15-20 minutes. If the fruit hasn’t broken down much after that time is up, use a potato masher (taking care not to burn yourself with hot jam) to break down the chunks.
Add the lemon juice and zest and continue cooking until the volume in the pot has reduced by approximately half and the jam passes your set test of choice (temperature, freezer, sheeting).
Remove the pot from the heat and 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. When 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.