Prepare a boiling water bath and 3 half-pint jars. Place 3 lids in a small saucepan of water and bring to a gentle simmer.
Bring a large pot of water to a boil. While it heats, cut the peaches in half and remove the pits. Fill a large bowl two-thirds of the way up with ice water. Blanch the peaches in the boiling water for 1 to 2 minutes, then immediately transfer to the ice water.
Once they are cool enough to touch, slip off the skins. Place the peaches in a shallow bowl or baking dish. Using a potato masher, smash them into a chunky pulp. Stir in the sugar and let the fruit sit for a few minutes, until the sugar is mostly dissolved.
To cook, scrape the fruit into a large skillet, add the salt, nutmeg and lemon juice, and place over medium-high heat. Stirring regularly, bring the fruit to a boil and cook until it bubbles and looks quite thick, 10 to 12 minutes. It's done when you pull a spatula through the jam and it doesn't immediately rush in to fill the space you've cleared.
Remove the jam from the heat and funnel into the prepared jars, leaving 1/2-inch of headspace. Wipe the rims, apply the lids and rings and process in a boiling water bath for 10 minutes.
Makes 3 half-pint jars.
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