In an 8-qt (7.6-l) stockpot over medium-high heat, warm the oil. Add the onion, carrot, fennel, and celery and cook, stirring occasionally, until softened and starting to brown, about 10 minutes. Season with a big pinch of salt.
Reduce the heat to medium-low and add the wine, stirring to scrape up the browned bits. Add the chicken stock; fish bones, heads, and bodies; star anise pods; b