01 - Preheat grill to medium heat (375°F).
02 - Season halibut fillets generously with salt and pepper on both sides.
03 - Place a heatproof skillet or grill-safe pan over medium heat. Add olive oil and sauté shallot and garlic until fragrant, about 1 minute.
04 - Add chopped tomatoes to the pan. Cook, stirring frequently, until tomatoes begin to break down, approximately 3-4 minutes.
05 - Pour in white wine and lemon juice. Allow mixture to simmer until slightly reduced, 2-3 minutes.
06 - Reduce heat to low. Whisk in butter one tablespoon at a time until fully incorporated and sauce achieves silky consistency. Stir in chopped fresh basil.
07 - Carefully place seasoned halibut fillets into the tomato-butter sauce. Spoon sauce over the top of each fillet to ensure even coating.
08 - Transfer skillet to preheated grill and close the lid. Poach fish in sauce for 8-12 minutes until just opaque throughout and flakes easily with a fork.
09 - For enhanced flavor and presentation, transfer fillets directly to grill grates for 1 minute per side to create signature grill marks.
10 - Arrange halibut on serving plates, spooning additional tomato-butter sauce over each fillet. Garnish generously with fresh basil leaves and serve with lemon wedges alongside.