Pour olive oil into a 4- to 6-quart pan over medium-high heat; add andouille sausages, sliced 1/4 inch thick, and stir often until beginning to brown. Add onion, peeled and chopped, and stir often until limp. Add saffron threads, chicken broth, and sweet potato, peeled and cut into 1/2-inch chunks. Bring to a boil, then reduce heat and simmer until sweet potato is barely tender when pierced, about 5 minutes. Stir in whipping cream and salt and pepper to taste.
Meanwhile, rinse halibut and pat dry; cut into 1-inch chunks. Lay chunks on top of soup, cover, and cook until halibut is opaque but still moist-looking in the center (cut a piece to check), about 10 minutes. Gently stir soup. Ladle into bowls and garnish with thinly sliced green onion.
Wine pairing: Arneis, a lively Italian white (the name means "little rascal"), is an almost perfect match for the halibut chowder, although a mineral-rich, aromatic dry Riesling works well too.