1. Follow steps 1 through 4 of Canning Instructions, using four wide-mouth quart-size jars.
2. Halve and pit peaches.
3. 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.
4. 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.
5. Arrange spices and peaches, cut sides down, equally in jars. Return syrup to boiling over high heat.
6. 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.