Combine the crushed peaches, cinnamon sticks, vanilla bean, molasses, and nutmeg in a large, non-reactive pot. Cook over medium heat, stirring often until the peaches are soft. This will take about 20 minutes or so.
Stir in the brown sugar, lemon juice, and 1/3 cup of the rum.
Bring it to a boil and cook until the sugar is completely dissolved.
Remove the vanilla bean and cinnamon sticks.
Use a blender or food processor to carefully purée the peach mixture.
Spread the peach mixture into a large shallow baking dish. I use two to make this go faster.
Bake the butter for 30 minutes and then give it a stir.
Continue to bake until the butter has thickened to a nice, thick consistency. Stir often so this doesn't stick. This will take about another hour or so.
If you divided the peach butter into 2 pans, combine them into one and add the remaining 1/3 c of dark rum. Stir well.
Ladle the hot peach rum butter into hot jars (pint, half pint, or 4 ounce) leaving 1/4 inch of head space.
Remove air bubbles with a bubble wand and adjust the level of butter to maintain the headspace.
Wipe the rim of the jar with a damp cloth that is dipped in white vinegar to remove any residue.
Close the jar with a lid and ring and place it into your canner. Repeat with all of the peach rum butter.
Process your jars for 10 minutes. (Adjust for Elevation - see article linked above)
After the jars are processed, transfer them to a line surface in a draft-free location.
Allow the jars to cool for 12-24 hours.
Remove the rings, test the seals, label, and store in your pantry.
Enjoy!
Notes
This recipe can vary greatly in how many jars you end up with, depending upon how much juice there is in your peaches. The more you have to cook them down to thicken the butter, the less you will end up with in the end. You could end up with anywhere between 5 half pint to 4 pints of the butter.