Combine first 6 ingredients in heavy medium saucepan. Bring to boil over high heat, stirring until sugar dissolves. Reduce heat to low, cover partially, and simmer gently until peaches are tender, about 15 minutes. Cool completely in saucepan. Discard star anise. (Sauce can be made 1 day ahead. Cover and refrigerate. Bring to room temperature before using.)
Scoop ice cream into dessert goblets. Spoon peach sauce over; sprinkle with pine nuts and serve immediately.
*Brown star-shaped seedpods available at Asian markets and specialty foods stores and in the spice section of some supermarkets.
