Drizzle 1 tablespoon of olive oil over the halibut and season with salt and pepper. Heat a grill pan over high heat. Cook the fish on the grill pan until just cooked through, about 4 minutes per side, depending on thickness.
In a medium saucepan, heat the 3 tablespoons of olive oil over medium-high heat. Add the shallots and cook for 1 minute. Add the garlic and artichokes and cook until golden brown, about 5 minutes. Add the white wine and stir, scraping the brown bits off the bottom of the pan with a wooden spoon. Add the chicken broth, tomatoes and juice, thyme, and 1/4 teaspoon each salt and pepper. Bring to a simmer.
Ladle the artichoke and tomato broth into shallow bowls. Top with the grilled halibut. Serve immediately.