01 - Preheat grill to medium heat, approximately 375°F.
02 - Generously season halibut fillets with kosher salt and freshly ground black pepper on both sides.
03 - Place a large heatproof skillet or grill-safe pan over medium heat. Add olive oil and sauté finely chopped shallot and minced 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 dry white wine and fresh lemon juice. Allow the mixture to simmer until slightly reduced, about 2-3 minutes.
06 - Reduce heat to low. Gradually whisk in unsalted butter, one tablespoon at a time, until sauce becomes silky and emulsified. Stir in finely chopped fresh basil.
07 - Carefully place seasoned halibut fillets into the tomato-butter sauce. Spoon sauce over the top of each fillet to coat.
08 - Transfer the skillet to the preheated grill and close the lid. Poach the fish in the sauce for 8-12 minutes, until just opaque and flakes easily with a fork.
09 - For enhanced flavor, carefully transfer fillets directly onto grill grates for 1 minute per side to achieve desirable grill marks.
10 - Plate the halibut with additional tomato-butter sauce spooned over each fillet. Garnish with fresh basil leaves and serve with lemon wedges on the side.