Step 1

Heat oil in a large skillet over medium-high heat. Add onion and ginger and cook, stirring occasionally, until golden brown, 8–10 minutes. Add star anise, bay leaves, cinnamon stick, sugar, cumin seeds, mustard seeds, paprika, and salt and cook, stirring, until fragrant, about 3 minutes. Add peaches and cook, stirring occasionally, until softened and beginning to release their juices (but still hold their shape), about 5 minutes. Let cool slightly.

Step 2

Serve with Kerala-Style Fried Chicken (click for recipe).

Step 3

DO AHEAD: Chutney can be made 5 days. Let cool; cover and chill.