Put the water, sugar and 200ml / scant 1 cup of the bourbon in a wide-bottomed saucepan, swirl about to help the sugar start dissolving a bit, and then put on the hob over medium heat and bring to the boil. Let it boil away for 5 minutes or so and then turn the heat down so that the syrup simmers; you want pronounced but not fierce bubbles.
Cut the peaches in half and remove the stones and then lower these halves, so that they fit snugly, cut side down, in the pan (I find I get four to six halves at a time, depending on the pan I’m using) and poach for a couple of minutes before turning them over and poaching for another 2-3 minutes cut side up; obviously, the ripeness of the peaches will determine exactly how long they need cooking. (And if the peaches are very unripe, it will be much easier to remove the stones after cooking.) The best way of testing the peaches is to prod the cut sides with a fork; you’ll be serving the fruit hump side up later and don’t want any fork marks to mar the pink-cheeked beauty of these pale-fleshed peaches.
When they feel tender but not flabbily soft, remove with a slotted spoon to a dish and continue till you’ve cooked all the peaches. Pour the juices that have collected in the plate – pink from the colour of the skins – back into the poaching liquid, itself blush-deepened from cooking the fruit, then measure 200ml / 1 scant cup of the liquid into a small saucepan. Add the remaining 50ml / 1 tablespoon of bourbon to this pan, put on the heat and boil till reduced by about half.
While this is happening, carefully peel off the skins; this should be easy enough. And on cooking, you’ll see that the rosy fuzz leaves behind its markings on the white fruit, so that each peach half is tenderly coloured with an uneven pink.
You can leave the peach halves, cut side down, covered with clingfilm, on a plate till you need them. Should the peaches start turning brown on standing, just spritz with lime and their unsullied beauty will be restored.
Let the reduced syrup cool in a jug somewhere nearby; you can freeze the remaining poaching liquid to use the next time you want to make these (just top up with water and a dash or two of bourbon when you reheat). Before serving, pour some of the thick, pink-bronze syrup over the peaches and scatter the torn-off mint leaves, some left whole, some roughly chopped, on top.