Place the peaches, bourbon, maple syrup, sugar, and vinegar in a large Dutch oven or other wide, heavy pot, and heat over medium heat. Cover and bring to a boil. Reduce heat to low, and simmer, stirring occasionally, until the peaches are very tender and losing their shape. Remove from heat, and use an immersion blender to purée into a smooth butter (or use a regular blender, being careful not to fill the pitcher more than halfway - you'll need to do this in batches - and hold a towel over the lid while the motor is running.)

Continue to cook the peach butter over medium-low heat, stirring frequently, until the butter has reduced to desired thickness. Taste and add more maple syrup, sugar, and bourbon if needed.

Set out 7 hot, sterilized, half-pint jars (see note) on a folded towel on a countertop. Ladle the peach butter into the jars, leaving 1/2-inch of head room. (Depending on how much you reduced the peach butter, you'll have between 6 and 7 half-pints.) Wipe the rims, and gently secure the lids and bands. Process in a boiling water bath for 10 minutes, starting the 10 minutes after the water returns to a boil. Transfer the jars to a folded towel on the counter and allow to cool at room temperature. After 1 hour, check the seals by removing the bands from the jars, then holding the jars by their lids. The lids should hold firm. If not, refrigerate that jar and eat promptly.

Store sealed jars in a cool, dark cupboard.