For the caponata: In a large skillet, heat the olive oil over medium-high heat. Add the onion and season with salt and pepper. Cook until translucent, about 3 minutes. Add the celery and artichoke hearts and cook until soft and the artichokes are lightly browned, 3 to 4 minutes. Add the tomatoes, olives, and raisins to the pan. Simmer over medium-low heat, stirring frequently, until the mixture thickens, about 25 minutes. Stir in the vinegar, sugar, and capers and season with salt and pepper, to taste.
For the halibut: Place a nonstick grill pan over medium-high heat or preheat a gas or charcoal grill. (If not using a nonstick grill pan, lightly oil the pan before grilling the fish. The halibut can also be roasted for 10 to 12 minutes in a pre-heated 400 degrees F oven.)
Drizzle the halibut on both sides with olive oil. Season on both sides with salt and pepper. Grill until the flesh flakes easily with a fork, 3 to 4 minutes on each side.
Arrange the halibut on a serving platter and top with the caponata. Garnish with chopped parsley and serve.
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