Fill a large pot with water, cover and bring to a boil. Add the canning jars, lids and rings along with a set of tongs and a ladle and simmer over low heat for about 10 minutes to sterilize. Cover the pot and turn off the heat.
Set a metal rack in another large pot. Fill the pot with water, cover and bring to a boil. Add the peaches and boil until the skins loosen, about 30 seconds. Using a slotted spoon, transfer the peaches to a large rimmed baking sheet and let cool. Peel the peaches, then halve and pit them and cut into 1/2-inch dice.
In a large skillet, combine the cider vinegar with the granulated and brown sugars and bring to a boil to dissolve the sugars. Add the shallot, currants, ginger, cumin seeds, lemongrass, coriander seeds, fennel seeds, curry leaves and bay leaves and simmer over moderate heat for 5 minutes. Add the peaches and simmer over moderate heat until tender, about 4 minutes. Discard the lemongrass, curry leaves and bay leaves. Stir in the cilantro and pink peppercorn and season with salt.
Using the sterilized tongs, remove the jars from the hot water and transfer them to a large rimmed baking sheet. Ladle the chutney into the jars, leaving 1/2 inch of space at the top. Using the tongs, place the lids on the jars followed by the rings. Screw on the lids securely but not too tightly.
Using canning tongs, lower the jars onto the rack in the pot of boiling water, making sure they are covered by at least 1 inch of water. Boil the jarred chutney over high heat for 15 minutes. Using the canning tongs, transfer the jars to a rack to cool until the lids seal (they will look concave); refrigerate any jars that do not seal. Store the chutney in a cool, dark place for up to 6 months; if the chutney separates, stir to combine before serving.