Heat a large nonstick skillet over medium-high heat. Add 2 1/4 teaspoons oil to pan; swirl to coat. Sprinkle halibut evenly with salt and black pepper. Add fish to pan; cook 3 minutes on each side or until fish flakes easily when tested with a fork or until desired degree of doneness. Carefully remove fish from pan, and keep warm.
Add remaining 2 1/4 teaspoons oil to pan; swirl to coat. Add shallots and garlic to pan; sauté 1 minute. Add bell pepper and next 3 ingredients (through paprika); sauté 3 minutes or until bell pepper is tender. Stir in parsley. Serve relish with fish.