1. Heat oil in a large pot over medium heat. Add garlic, capers, and lemon zest and stir just until fragrant, about 30 seconds.
2. Add wine and simmer, until reduced by half, about 2 minutes. Add broth and potatoes and return to a simmer. Lower heat slightly to maintain simmer, cover, and cook 10 minutes.
3. Meanwhile, sprinkle halibut with salt and pepper.
4. Add artichokes and halibut chunks to pot and stir. Cover and cook until potatoes are tender when pierced and halibut is opaque in the center, 8 to 10 minutes. Stir in parsley, lemon juice to taste, and olives. Season with additional salt and pepper to taste. Serve hot, with lemon wedges on the side.