Prepare a boiling water bath canner and enough jars to hold 4 1/2 to 5 pints of product
Heap the apples into a large pot with a tight-fitting lid. Add the ginger and water and set the pot on the stove over medium-high heat. Once you see some steam escaping from the pan, reduce the heat to medium-low. Continue to cook until the apples are completely tender.
When the apples are fork tender, use an immersion blender to puree them smooth. Increase the heat to medium and cook for 15 to 20 minutes, stirring regularly, until the applesauce turns the color of wildflower honey.
At this point, add the sugar and continue to cook for another 10 minutes or so. The preserve may start to splash a little as it cooks down. If that happens, pull out your trusty splatter shield and set it on top of the pot. If you don't have a splatter shield, another option is to finish cooking the butter in the oven at 300F for half an hour or so.
When the butter is light but spreadable, it is done. Taste it and add some lemon juice if you feel like the sweetness needs some balance.
Once you've decided that it's done, funnel the finished butter into your 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 lid from the pot and slide it off the hot burner. Let the jars cool gradually in the water to help prevent the product from siphoning.
Finally, remove the jars from the canner and set them on a folded kitchen towel to cool.
Sealed jars can be stored at room temperature and will keep for a couple of years. Any unsealed jars should be refrigerated and used promptly.