Follow steps 1 through 4 of Canning Instructions, using four wide-mouth quart-size jars.
Halve and pit peaches.
In a 6- to 8-quart pan, combine sugar, vinegar, allspice, peppercorns, cinnamon sticks, cardamom, and star anise. Stir over high heat until boiling; reduce heat, cover, and simmer for 5 minutes, stirring occasionally.
Turn heat under sugar mixture to high. Add 1/3 of peaches, cover, and stir occasionally until mixture returns to a boil and peaches are barely tender when pierced, 2 to 3 minutes. With a slotted spoon, transfer peaches to a large bowl. Repeat to cook remaining peaches. Remove syrup from heat.
Arrange spices and peaches, cut sides down, equally in jars. Return syrup to boiling over high heat.
Follow steps 5 through 11 of Canning Instructions, ladling hot syrup over peaches, leaving 1/2 inch of headspace in each jar, and processing jars for 25 minutes (see notes). Chill any extra syrup airtight up to 2 weeks.
Note: Nutritional analysis is per 1/2 cup.