Cut squash in half; scoop out seeds.
With a vegetable peeler, pare green skin from squash; discard. Using a slicer or knife, cut squash into 1/8-inch-thick slices (makes about 6 cups); rinse slices.
In a 4- to 5-quart pan, combine vinegar, mirin, ginger, and anise. Bring to boiling over high heat, then reduce heat and simmer 5 minutes. Add squash and return to boiling over high heat.
Transfer spiced mixture to a jar. Let cool and serve, or cover and chill up to 4 weeks.
Nutritional analysis per 1/4 cup drained serving.