Prepare a boiling water bath canner and 7 half pint jars.

Cut the peaches into quarters and remove the pits. Heap the peach pieces into a heatproof bowl and put the bowl in the sink.

Bring a kettle of water to a boil. Once it's hot, pour the hot water onto the peaches. Cover the bowl with a pot lid or sheet pan and let the peaches sit for 3 to 4 minutes. When the time is up, carefully tip most of the hot water out into the sink. Run cold tap water over the peaches until they're cool enough to handle.

Remove the peels from the peaches and cut each quarter into 2 to 3 slices. Place the peeled peach slices into a medium, non-reactive pan.

Add the sugar, lemon zest and juice, and the nutmeg to the peaches and stir to combine. Let it sit for 15 or 20 minutes, until the sugar has dissolved and the fruit is juicy.

Set the pot on the stove over high heat. Bring to a boil and then reduce the heat to medium-high.

Cook, stirring regularly, until the conserve has thickened and reduced by about a third.

Near the end of cooking, stir in the walnuts.

When you're happy with the consistency of the conserve, remove the pot from the heat.

Funnel the conserve into the prepared jars. Wipe the rims, apply the lids and rings, and process in a boiling water bath canner for 15 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.