Place peaches, garlic, ginger and vinegar in a large, heavy-based saucepan and cook over medium-high heat until boiling. Continue cooking for 5-10 minutes, stirring regularly until the fruit begins to soften.
Add the rest of the ingredients, reduce the heat to medium-low, until you get a slow regular bubbling, then cook 30-40 minutes until thick and sticky, stirring often.
Hunt down and remove the star anise, ladle into hot, sterile jars. Seal well and label.
Store in a cool, dark place for 3-4 weeks to allow the flavours to mature before using.